Abstract

We investigate the stability of incoherently coupled two-color vector dark and grey solitons in a nonlinear self-defocusing media. We employ the variational technique to derive approximate solutions of the two-color vector dark solitons. The relations between the soliton parameters and the representation of the transverse velocities of the vector solitons are analytically obtained. We also demonstrate numerically the propagation dynamics of the two-color vector solitons, which shows that the two-color vector dark and grey solitons with different wavelengths are always unstable.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  43. A. Sukhinin, A. B. Aceves, J.-C. Diels, and L. Arissian, “Collapse events of two-color optical beams,” Phys. Rev. A 95(3), 031801(R) (2017).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  50. I. V. Barashenkov, “Stability criterion for dark solitons,” Phys. Rev. Lett. 77(7), 1193–1197 (1996).
    [Crossref] [PubMed]
  51. M Facão and MI Carvalho, “Stability of dark screening solitons in photorefractive media,” Theor. Math. Phys. 160(1), 917–924 (2009).
    [Crossref]
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    [Crossref]
  53. G. Assanto, J. Michael, L. MacNeil, and N. F. Smyth, “Diffraction-induced instability of coupled dark solitary waves,” Opt. Lett. 40(8), 1771–1774 (2015).
    [Crossref] [PubMed]

2017 (2)

F. Baronio, S. Chen, and D. Mihalache, “Two-color walking Peregrine solitary waves,” Opt. Lett. 42(18), 3514–3517 (2017).
[Crossref] [PubMed]

A. Sukhinin, A. B. Aceves, J.-C. Diels, and L. Arissian, “Collapse events of two-color optical beams,” Phys. Rev. A 95(3), 031801(R) (2017).
[Crossref]

2016 (1)

J. Doussot, P. Bejot, and O. Faucher, “Two-color resonant filamentation in gases,” Phys. Rev. A 94(1), 013805 (2016).
[Crossref]

2015 (3)

2014 (1)

2013 (3)

L. Chen, Q. Wang, M. Shen, H. Zhao, Y.-Y. Lin, C.-C. Jeng, R.-K. Lee, and W. Krolikowski, “Nonlocal dark solitons under competing cubic-quintic nonlinearities,” Opt. Lett. 38(1), 13–15 (2013).
[Crossref] [PubMed]

Q. Kong, M. Shen, Z. Chen, Q. Wang, Ray-Kuang Lee, and W. Krolikowski, “Dark solitons in nonlocal media with competing nonlinearities,” Phys. Rev. A 87(6), 063832 (2013).
[Crossref]

W. Chen, Q. Kong, M. Shen, Q. Wang, and J. Shi, “Polarized vector dark solitons in nonlocal Kerr-type self-defocusing media,” Phys. Rev. A 87(1), 013809 (2013).
[Crossref]

2010 (1)

2009 (7)

M Facão and MI Carvalho, “Stability of dark screening solitons in photorefractive media,” Theor. Math. Phys. 160(1), 917–924 (2009).
[Crossref]

J. Yang, “Newton-conjugate gradient methods for solitary wave computations,” J. Comp. Phys. 228(18), 7007–7024 (2009).
[Crossref]

A. A. Minzoni, N. F. Smyth, Z. Xu, and Y. S. Kivshar, “Stabilization of vortex-soliton beams in nematic liquid crystals,” Phys. Rev. A 79(6), 063808 (2009).
[Crossref]

M. I. Molina and Y. S. Kivshar, “Two-color surface solitons in two-dimensional quadratic photonic lattices,” J. Opt. Soc. Am. B 26(8), 1545–1548 (2009).
[Crossref]

Z. Xu, M. I. Molina, and Y. S. Kivshar, “Interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80(5), 053827 (2009).
[Crossref]

W.-W. Hsiang, C.-H. Chang, C.-P. Cheng, and Y. Lai, “Passive synchronization between a self-similar pulse and a bound-soliton bunch in a two-color mode-locked fiber laser,” Opt. Lett. 34(13), 1967–1969 (2009).
[Crossref] [PubMed]

X. Zeng, S. Ashihara, Z. Wang, T. Wang, Y. Chen, and M. Cha, “Excitation of two-colored temporal solitons in a segmented quasi-phase-matching structure,” Opt. Express 17(19), 16877–16884 (2009).
[Crossref] [PubMed]

2008 (3)

Ming Shen, Qian Kong, Jielong Shi, and Qi Wang, “Incoherently coupled two-color Manakov vector solitons in nonlocal media,” Phys. Rev. A 77(1), 015811 (2008).
[Crossref]

B. D. Skuse and N. F. Smyth, “Two-color vector-soliton interactions in nematic liquid crystals in the local response regime,” Phys. Rev. A 77(1), 013817 (2008).
[Crossref]

G. Assanto, N. F. Smyth, and A. L. Worthy, “Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals,” Phys. Rev. A 78(1), 013832 (2008).
[Crossref]

2007 (2)

H. Susanto, P. G. Kevrekidis, R. Carretero-Gonzalez, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99(21), 214103 (2007).
[Crossref]

R. Radhakrishnan and K. Aravinthan, “Spatial vector soliton and its collisions in isotropic self-defocusing Kerr media,” Phys. Rev. E 75(2), 066605 (2007).
[Crossref]

2006 (2)

B. Prinari, M. J. Ablowitz, and G. Biondini, “Inverse scattering transform for the vector nonlinear Schrodinger equation with non-vanishing boundary conditions,” J. Math. Phys. 47(6), 063508 (2006).
[Crossref]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97(15), 153903 (2006).
[Crossref] [PubMed]

2005 (1)

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71(1), 016616 (2005).
[Crossref]

2004 (3)

D. V. Skryabin, F. Biancalana, D. M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett. 93(14), 143907 (2004).
[Crossref] [PubMed]

Y. V. Kartashov, A. A. Egorov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, “Stable multicolor periodic-wave arrays,” Phys. Rev. Lett. 92(3), 033901 (2004).
[Crossref] [PubMed]

I. E. Papacharalampous, P. G. Kevrekidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Elliptic dark solitons,” Phys. Scr. 69(1), 7–14 (2004).
[Crossref]

2002 (1)

Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89(27), 273902 (2002).
[Crossref]

1999 (2)

1998 (2)

1997 (3)

A. P. Sheppard and Y. S. Kivshar, “Polarized dark solitons in isotropic Kerr media,” Phys. Rev. E 55(4), 4773–4782 (1997).
[Crossref]

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. S. Kivshar, “Coupled photorefractive spatial-soliton pairs,” J. Opt. Soc. Am. B 14(11), 3066–3077 (1997).
[Crossref]

A. P. Sheppard and Yu. S. Kivshar, “Polarized dark solitons in isotropic Kerr media,” Phys. Rev. E 55(4), 4773–4782 (1997).
[Crossref]

1996 (2)

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76(20), 3699–3702 (1996).
[Crossref] [PubMed]

I. V. Barashenkov, “Stability criterion for dark solitons,” Phys. Rev. Lett. 77(7), 1193–1197 (1996).
[Crossref] [PubMed]

1995 (5)

Yuri S. Kivshar and W. Krolikowski, “Lagrangian approach for dark solitons,” Opt. Commun. 114(3–4), 353–362 (1995).
[Crossref]

R. Radhakrishnan and M. Lakshmanan, “Bright and dark soliton solutions to coupled nonlinear Schrodinger equations,” J. Phys. A 28(9), 2683–2692 (1995).
[Crossref]

H. T. Tran and R.A. Sammut, “Instability of two-frequency dark waves in self-defocussing media,” Opt. Commun. 119(5–6), 583–586 (1995).
[Crossref]

H. T. Tran and R. A. Sammut, “Families of multiwavelength spatial solitons in nonlinear Kerr media,” Phys. Rev. A 52(4), 3170–3175 (1995).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[Crossref] [PubMed]

1994 (4)

A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19(20), 1612–1614 (1994).
[Crossref] [PubMed]

H. T. Tran, R.A. Sammut, and W. Samir, “Multi-frequency spatial solitons in kerr media,” Opt. Commun. 113(1–3), 292–304 (1994).
[Crossref]

M. Haelterman and A. P. Sheppard, “Bifurcations of the dark soliton and polarization domain walls in nonlinear dispersive media,” Phys. Rev. E 49(5), 4512–4518 (1994).
[Crossref]

M. Haelterman and A. E Sheppard, “Extended modulational instability and new type of solitary wave in coupled nonlinear Schrodinger equations,” Phys. Lett. A 185(3), 265–272 (1994).
[Crossref]

1993 (2)

Yuri S. Kivshar, “Dark solitons in nonlinear optics,” IEEE J. Quantum Electron 29(1), 250–264 (1993).
[Crossref]

Yu. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18(5), 337–339 (1993).
[Crossref] [PubMed]

1991 (1)

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66(12), 1583–1586 (1991).
[Crossref] [PubMed]

1974 (1)

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Phys. JEPT 38, 248–253 (1974).

Ablowitz, M. J.

B. Prinari, M. J. Ablowitz, and G. Biondini, “Inverse scattering transform for the vector nonlinear Schrodinger equation with non-vanishing boundary conditions,” J. Math. Phys. 47(6), 063508 (2006).
[Crossref]

Aceves, A. B.

A. Sukhinin, A. B. Aceves, J.-C. Diels, and L. Arissian, “Collapse events of two-color optical beams,” Phys. Rev. A 95(3), 031801(R) (2017).
[Crossref]

A. Sukhinin, A. B. Aceves, J.-C. Diels, and L. Arissian, “On the co-existence of IR and UV optical filaments,” J. Phys. B: At. Mol. Opt. Phys. 48(9), 094021 (2015).
[Crossref]

Agrawal, G. P.

Yuri S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic Press, (2003).

Aitchison, J. S.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76(20), 3699–3702 (1996).
[Crossref] [PubMed]

Akhmediev, N. N.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76(20), 3699–3702 (1996).
[Crossref] [PubMed]

Alberucci, A.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97(15), 153903 (2006).
[Crossref] [PubMed]

Andersen, D. R.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66(12), 1583–1586 (1991).
[Crossref] [PubMed]

Aravinthan, K.

R. Radhakrishnan and K. Aravinthan, “Spatial vector soliton and its collisions in isotropic self-defocusing Kerr media,” Phys. Rev. E 75(2), 066605 (2007).
[Crossref]

Arissian, L.

A. Sukhinin, A. B. Aceves, J.-C. Diels, and L. Arissian, “Collapse events of two-color optical beams,” Phys. Rev. A 95(3), 031801(R) (2017).
[Crossref]

A. Sukhinin, A. B. Aceves, J.-C. Diels, and L. Arissian, “On the co-existence of IR and UV optical filaments,” J. Phys. B: At. Mol. Opt. Phys. 48(9), 094021 (2015).
[Crossref]

Ashihara, S.

Assanto, G.

G. Assanto, J. Michael, L. MacNeil, and N. F. Smyth, “Diffraction-induced instability of coupled dark solitary waves,” Opt. Lett. 40(8), 1771–1774 (2015).
[Crossref] [PubMed]

Y. Izdebskaya, G. Assanto, and W. Krolikowski, “Observation of stable-vector vortex solitons,” Opt. Lett. 40(17), 4182–4185 (2015).
[Crossref] [PubMed]

G. Assanto, N. F. Smyth, and A. L. Worthy, “Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals,” Phys. Rev. A 78(1), 013832 (2008).
[Crossref]

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97(15), 153903 (2006).
[Crossref] [PubMed]

Bang, O.

Barashenkov, I. V.

I. V. Barashenkov, “Stability criterion for dark solitons,” Phys. Rev. Lett. 77(7), 1193–1197 (1996).
[Crossref] [PubMed]

Baronio, F.

Bejot, P.

J. Doussot, P. Bejot, and O. Faucher, “Two-color resonant filamentation in gases,” Phys. Rev. A 94(1), 013805 (2016).
[Crossref]

Benabid, F.

D. V. Skryabin, F. Biancalana, D. M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett. 93(14), 143907 (2004).
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D. V. Skryabin, F. Biancalana, D. M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett. 93(14), 143907 (2004).
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B. Prinari, M. J. Ablowitz, and G. Biondini, “Inverse scattering transform for the vector nonlinear Schrodinger equation with non-vanishing boundary conditions,” J. Math. Phys. 47(6), 063508 (2006).
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Bird, D. M.

D. V. Skryabin, F. Biancalana, D. M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett. 93(14), 143907 (2004).
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Carretero-Gonzalez, R.

H. Susanto, P. G. Kevrekidis, R. Carretero-Gonzalez, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99(21), 214103 (2007).
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M Facão and MI Carvalho, “Stability of dark screening solitons in photorefractive media,” Theor. Math. Phys. 160(1), 917–924 (2009).
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Chang, C.-H.

Chen, L.

Chen, S.

Chen, W.

W. Chen, M. Shen, Q. Kong, J. Shi, Q. Wang, and W. Krolikowski, “Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities,” Opt. Lett. 39(7), 1764–1767 (2014).
[Crossref] [PubMed]

W. Chen, Q. Kong, M. Shen, Q. Wang, and J. Shi, “Polarized vector dark solitons in nonlocal Kerr-type self-defocusing media,” Phys. Rev. A 87(1), 013809 (2013).
[Crossref]

Chen, Y.

Chen, Z.

Q. Kong, M. Shen, Z. Chen, Q. Wang, Ray-Kuang Lee, and W. Krolikowski, “Dark solitons in nonlocal media with competing nonlinearities,” Phys. Rev. A 87(6), 063832 (2013).
[Crossref]

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. S. Kivshar, “Coupled photorefractive spatial-soliton pairs,” J. Opt. Soc. Am. B 14(11), 3066–3077 (1997).
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Cheng, C.-P.

Christodoulides, D. N.

Coskun, T. H.

Crasovan, L.-C.

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71(1), 016616 (2005).
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Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89(27), 273902 (2002).
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A. Sukhinin, A. B. Aceves, J.-C. Diels, and L. Arissian, “Collapse events of two-color optical beams,” Phys. Rev. A 95(3), 031801(R) (2017).
[Crossref]

A. Sukhinin, A. B. Aceves, J.-C. Diels, and L. Arissian, “On the co-existence of IR and UV optical filaments,” J. Phys. B: At. Mol. Opt. Phys. 48(9), 094021 (2015).
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J. Doussot, P. Bejot, and O. Faucher, “Two-color resonant filamentation in gases,” Phys. Rev. A 94(1), 013805 (2016).
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A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97(15), 153903 (2006).
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Y. V. Kartashov, A. A. Egorov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, “Stable multicolor periodic-wave arrays,” Phys. Rev. Lett. 92(3), 033901 (2004).
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M Facão and MI Carvalho, “Stability of dark screening solitons in photorefractive media,” Theor. Math. Phys. 160(1), 917–924 (2009).
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J. Doussot, P. Bejot, and O. Faucher, “Two-color resonant filamentation in gases,” Phys. Rev. A 94(1), 013805 (2016).
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H. Susanto, P. G. Kevrekidis, R. Carretero-Gonzalez, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99(21), 214103 (2007).
[Crossref]

I. E. Papacharalampous, P. G. Kevrekidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Elliptic dark solitons,” Phys. Scr. 69(1), 7–14 (2004).
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Haelterman, M.

M. Haelterman and A. P. Sheppard, “Bifurcations of the dark soliton and polarization domain walls in nonlinear dispersive media,” Phys. Rev. E 49(5), 4512–4518 (1994).
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M. Haelterman and A. E Sheppard, “Extended modulational instability and new type of solitary wave in coupled nonlinear Schrodinger equations,” Phys. Lett. A 185(3), 265–272 (1994).
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W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
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Izdebskaya, Y.

Jeng, C.-C.

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A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97(15), 153903 (2006).
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J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76(20), 3699–3702 (1996).
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G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66(12), 1583–1586 (1991).
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Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71(1), 016616 (2005).
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Y. V. Kartashov, A. A. Egorov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, “Stable multicolor periodic-wave arrays,” Phys. Rev. Lett. 92(3), 033901 (2004).
[Crossref] [PubMed]

Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89(27), 273902 (2002).
[Crossref]

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H. Susanto, P. G. Kevrekidis, R. Carretero-Gonzalez, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99(21), 214103 (2007).
[Crossref]

I. E. Papacharalampous, P. G. Kevrekidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Elliptic dark solitons,” Phys. Scr. 69(1), 7–14 (2004).
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Z. Xu, M. I. Molina, and Y. S. Kivshar, “Interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80(5), 053827 (2009).
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A. A. Minzoni, N. F. Smyth, Z. Xu, and Y. S. Kivshar, “Stabilization of vortex-soliton beams in nematic liquid crystals,” Phys. Rev. A 79(6), 063808 (2009).
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M. I. Molina and Y. S. Kivshar, “Two-color surface solitons in two-dimensional quadratic photonic lattices,” J. Opt. Soc. Am. B 26(8), 1545–1548 (2009).
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Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. S. Kivshar, “Coupled photorefractive spatial-soliton pairs,” J. Opt. Soc. Am. B 14(11), 3066–3077 (1997).
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A. P. Sheppard and Y. S. Kivshar, “Polarized dark solitons in isotropic Kerr media,” Phys. Rev. E 55(4), 4773–4782 (1997).
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A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19(20), 1612–1614 (1994).
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A. P. Sheppard and Yu. S. Kivshar, “Polarized dark solitons in isotropic Kerr media,” Phys. Rev. E 55(4), 4773–4782 (1997).
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W. Chen, M. Shen, Q. Kong, J. Shi, Q. Wang, and W. Krolikowski, “Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities,” Opt. Lett. 39(7), 1764–1767 (2014).
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W. Chen, Q. Kong, M. Shen, Q. Wang, and J. Shi, “Polarized vector dark solitons in nonlocal Kerr-type self-defocusing media,” Phys. Rev. A 87(1), 013809 (2013).
[Crossref]

Q. Kong, M. Shen, Z. Chen, Q. Wang, Ray-Kuang Lee, and W. Krolikowski, “Dark solitons in nonlocal media with competing nonlinearities,” Phys. Rev. A 87(6), 063832 (2013).
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Ming Shen, Qian Kong, Jielong Shi, and Qi Wang, “Incoherently coupled two-color Manakov vector solitons in nonlocal media,” Phys. Rev. A 77(1), 015811 (2008).
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Lai, Y.

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Lee, Ray-Kuang

Q. Kong, M. Shen, Z. Chen, Q. Wang, Ray-Kuang Lee, and W. Krolikowski, “Dark solitons in nonlocal media with competing nonlinearities,” Phys. Rev. A 87(6), 063832 (2013).
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Luther-Davies, Barry

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Maillotte, H.

Malomed, B. A.

H. Susanto, P. G. Kevrekidis, R. Carretero-Gonzalez, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99(21), 214103 (2007).
[Crossref]

I. E. Papacharalampous, P. G. Kevrekidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Elliptic dark solitons,” Phys. Scr. 69(1), 7–14 (2004).
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Mihalache, D.

F. Baronio, S. Chen, and D. Mihalache, “Two-color walking Peregrine solitary waves,” Opt. Lett. 42(18), 3514–3517 (2017).
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Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71(1), 016616 (2005).
[Crossref]

Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89(27), 273902 (2002).
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Millot, G.

Minzoni, A. A.

A. A. Minzoni, N. F. Smyth, Z. Xu, and Y. S. Kivshar, “Stabilization of vortex-soliton beams in nematic liquid crystals,” Phys. Rev. A 79(6), 063808 (2009).
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Molina, M. I.

M. I. Molina and Y. S. Kivshar, “Two-color surface solitons in two-dimensional quadratic photonic lattices,” J. Opt. Soc. Am. B 26(8), 1545–1548 (2009).
[Crossref]

Z. Xu, M. I. Molina, and Y. S. Kivshar, “Interface solitons in quadratic nonlinear photonic lattices,” Phys. Rev. A 80(5), 053827 (2009).
[Crossref]

Nistazakis, H. E.

I. E. Papacharalampous, P. G. Kevrekidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Elliptic dark solitons,” Phys. Scr. 69(1), 7–14 (2004).
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Papacharalampous, I. E.

I. E. Papacharalampous, P. G. Kevrekidis, H. E. Nistazakis, D. J. Frantzeskakis, and B. A. Malomed, “Elliptic dark solitons,” Phys. Scr. 69(1), 7–14 (2004).
[Crossref]

Peccianti, M.

A. Alberucci, M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, “Two-color vector solitons in nonlocal media,” Phys. Rev. Lett. 97(15), 153903 (2006).
[Crossref] [PubMed]

Prinari, B.

B. Prinari, M. J. Ablowitz, and G. Biondini, “Inverse scattering transform for the vector nonlinear Schrodinger equation with non-vanishing boundary conditions,” J. Math. Phys. 47(6), 063508 (2006).
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R. Radhakrishnan and M. Lakshmanan, “Bright and dark soliton solutions to coupled nonlinear Schrodinger equations,” J. Phys. A 28(9), 2683–2692 (1995).
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Regan, J. J.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66(12), 1583–1586 (1991).
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H. T. Tran, R.A. Sammut, and W. Samir, “Multi-frequency spatial solitons in kerr media,” Opt. Commun. 113(1–3), 292–304 (1994).
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Sammut, R. A.

H. T. Tran and R. A. Sammut, “Families of multiwavelength spatial solitons in nonlinear Kerr media,” Phys. Rev. A 52(4), 3170–3175 (1995).
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Sammut, R.A.

H. T. Tran and R.A. Sammut, “Instability of two-frequency dark waves in self-defocussing media,” Opt. Commun. 119(5–6), 583–586 (1995).
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H. T. Tran, R.A. Sammut, and W. Samir, “Multi-frequency spatial solitons in kerr media,” Opt. Commun. 113(1–3), 292–304 (1994).
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G. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
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Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. S. Kivshar, “Coupled photorefractive spatial-soliton pairs,” J. Opt. Soc. Am. B 14(11), 3066–3077 (1997).
[Crossref]

Seve, E.

Shen, M.

W. Chen, M. Shen, Q. Kong, J. Shi, Q. Wang, and W. Krolikowski, “Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities,” Opt. Lett. 39(7), 1764–1767 (2014).
[Crossref] [PubMed]

L. Chen, Q. Wang, M. Shen, H. Zhao, Y.-Y. Lin, C.-C. Jeng, R.-K. Lee, and W. Krolikowski, “Nonlocal dark solitons under competing cubic-quintic nonlinearities,” Opt. Lett. 38(1), 13–15 (2013).
[Crossref] [PubMed]

Q. Kong, M. Shen, Z. Chen, Q. Wang, Ray-Kuang Lee, and W. Krolikowski, “Dark solitons in nonlocal media with competing nonlinearities,” Phys. Rev. A 87(6), 063832 (2013).
[Crossref]

W. Chen, Q. Kong, M. Shen, Q. Wang, and J. Shi, “Polarized vector dark solitons in nonlocal Kerr-type self-defocusing media,” Phys. Rev. A 87(1), 013809 (2013).
[Crossref]

Shen, Ming

Ming Shen, Qian Kong, Jielong Shi, and Qi Wang, “Incoherently coupled two-color Manakov vector solitons in nonlocal media,” Phys. Rev. A 77(1), 015811 (2008).
[Crossref]

Sheppard, A. E

M. Haelterman and A. E Sheppard, “Extended modulational instability and new type of solitary wave in coupled nonlinear Schrodinger equations,” Phys. Lett. A 185(3), 265–272 (1994).
[Crossref]

Sheppard, A. P.

A. P. Sheppard and Yu. S. Kivshar, “Polarized dark solitons in isotropic Kerr media,” Phys. Rev. E 55(4), 4773–4782 (1997).
[Crossref]

A. P. Sheppard and Y. S. Kivshar, “Polarized dark solitons in isotropic Kerr media,” Phys. Rev. E 55(4), 4773–4782 (1997).
[Crossref]

M. Haelterman and A. P. Sheppard, “Bifurcations of the dark soliton and polarization domain walls in nonlinear dispersive media,” Phys. Rev. E 49(5), 4512–4518 (1994).
[Crossref]

Shi, J.

W. Chen, M. Shen, Q. Kong, J. Shi, Q. Wang, and W. Krolikowski, “Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities,” Opt. Lett. 39(7), 1764–1767 (2014).
[Crossref] [PubMed]

W. Chen, Q. Kong, M. Shen, Q. Wang, and J. Shi, “Polarized vector dark solitons in nonlocal Kerr-type self-defocusing media,” Phys. Rev. A 87(1), 013809 (2013).
[Crossref]

Shi, Jielong

Ming Shen, Qian Kong, Jielong Shi, and Qi Wang, “Incoherently coupled two-color Manakov vector solitons in nonlocal media,” Phys. Rev. A 77(1), 015811 (2008).
[Crossref]

Skryabin, D. V.

D. V. Skryabin, F. Biancalana, D. M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett. 93(14), 143907 (2004).
[Crossref] [PubMed]

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B. D. Skuse and N. F. Smyth, “Two-color vector-soliton interactions in nematic liquid crystals in the local response regime,” Phys. Rev. A 77(1), 013817 (2008).
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Smyth, N. F.

G. Assanto, J. Michael, L. MacNeil, and N. F. Smyth, “Diffraction-induced instability of coupled dark solitary waves,” Opt. Lett. 40(8), 1771–1774 (2015).
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A. A. Minzoni, N. F. Smyth, Z. Xu, and Y. S. Kivshar, “Stabilization of vortex-soliton beams in nematic liquid crystals,” Phys. Rev. A 79(6), 063808 (2009).
[Crossref]

B. D. Skuse and N. F. Smyth, “Two-color vector-soliton interactions in nematic liquid crystals in the local response regime,” Phys. Rev. A 77(1), 013817 (2008).
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G. Assanto, N. F. Smyth, and A. L. Worthy, “Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals,” Phys. Rev. A 78(1), 013832 (2008).
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G. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
[Crossref] [PubMed]

Stegeman, G. I.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76(20), 3699–3702 (1996).
[Crossref] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[Crossref] [PubMed]

Sukhinin, A.

A. Sukhinin, A. B. Aceves, J.-C. Diels, and L. Arissian, “Collapse events of two-color optical beams,” Phys. Rev. A 95(3), 031801(R) (2017).
[Crossref]

A. Sukhinin, A. B. Aceves, J.-C. Diels, and L. Arissian, “On the co-existence of IR and UV optical filaments,” J. Phys. B: At. Mol. Opt. Phys. 48(9), 094021 (2015).
[Crossref]

Susanto, H.

H. Susanto, P. G. Kevrekidis, R. Carretero-Gonzalez, B. A. Malomed, and D. J. Frantzeskakis, “Mobility of discrete solitons in quadratically nonlinear media,” Phys. Rev. Lett. 99(21), 214103 (2007).
[Crossref]

Swartzlander, G. A.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66(12), 1583–1586 (1991).
[Crossref] [PubMed]

Sylvestre, T.

Torner, L.

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71(1), 016616 (2005).
[Crossref]

Y. V. Kartashov, A. A. Egorov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, “Stable multicolor periodic-wave arrays,” Phys. Rev. Lett. 92(3), 033901 (2004).
[Crossref] [PubMed]

Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89(27), 273902 (2002).
[Crossref]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[Crossref] [PubMed]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74(25), 5036–5039 (1995).
[Crossref] [PubMed]

Tran, H. T.

H. T. Tran and R. A. Sammut, “Families of multiwavelength spatial solitons in nonlinear Kerr media,” Phys. Rev. A 52(4), 3170–3175 (1995).
[Crossref] [PubMed]

H. T. Tran and R.A. Sammut, “Instability of two-frequency dark waves in self-defocussing media,” Opt. Commun. 119(5–6), 583–586 (1995).
[Crossref]

H. T. Tran, R.A. Sammut, and W. Samir, “Multi-frequency spatial solitons in kerr media,” Opt. Commun. 113(1–3), 292–304 (1994).
[Crossref]

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G. Assanto, N. F. Smyth, and A. L. Worthy, “Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals,” Phys. Rev. A 78(1), 013832 (2008).
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Figures (9)

Fig. 1
Fig. 1 Width (∝ D−1) of the two-color vector dark solitons versus the nonresonant coefficient γ with different values of B1 and B2.
Fig. 2
Fig. 2 Transverse velocities of the two-color vector dark solitons versus the nonresonant coefficient γ when B1 = B2. The dashed and solid lines represent the transverse velocities v1 and v2 of two soliton components E1 and E2, respectively.
Fig. 3
Fig. 3 Transverse velocities of the two-color vector dark solitons versus the nonresonant coefficient γ when B1B2. The dashed and solid lines represent the transverse velocities v1 and v2 of two soliton components E1 and E2, respectively.
Fig. 4
Fig. 4 Numerical solutions ψ(x) and ϕ(x) of the two-color vector dark solitons with different nonresonant coefficients (a) γ = 1 and (b) γ = 1.02, respectively.
Fig. 5
Fig. 5 Dynamics of two-color vector dark solitons (a) and its two components E1 (c), E2 (d) in nonlinear media. The intensity profiles of the vector solitons (b) at the beginning (z = 0) and the end (z = 10) of the propagation distance. The initial parameters are B1 = B2 = 1 and γ = 1.
Fig. 6
Fig. 6 Dynamics of two-color vector dark solitons (a) and its two components E1 (c), E2 (d) in nonlinear media. The intensity profiles of the vector solitons (b) at a particular propagation distance z = 4 and the end of the propagation distance z = 10. The initial parameters are B1 = B2 = 1 and γ = 1.02.
Fig. 7
Fig. 7 Dynamics of two-color vector grey solitons (a) and its two components E1 (c), E2 (d) in nonlinear media. The intensity profiles of the vector solitons at the beginning (z = 0) and the end (z = 10) of the propagation distance. The initial parameters are B1 = B2 = 0.8 and γ = 1.
Fig. 8
Fig. 8 Dynamics of two-color vector grey solitons (a) and its two components E1 (c), E2 (d) in nonlinear media. The intensity profiles of the vector solitons (b) at a particular propagation distance z = 4 and the end of the propagation distance z = 10. The initial parameters are B1 = B2 = 0.8 and γ = 1.02.
Fig. 9
Fig. 9 Dynamics of one-color (γ = 1) vector grey solitons (a) and its two components E1 (c), E2 (d) in nonlinear media. The intensity profiles of the vector solitons (b) at a particular propagation distance z = 4 and the end of the propagation distance z = 10. The initial parameters are B1 = 0.8, B2 = 0.796 and γ = 1.

Equations (13)

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i E 1 z + γ 2 2 E 1 x 2 1 γ ( | E 1 | 2 + 2 | E 2 | 2 ) E 1 = 0 ,
i E 2 z + 1 2 2 E 2 x 2 ( 2 | E 1 | 2 + | E 2 | 2 ) E 2 = 0 ,
E 1 = B 1 tanh [ D ( x x 1 ) ] + i A 1 ,
E 2 = B 2 tanh [ D ( x x 2 ) ] + i A 2 .
L ˜ 1 = i 2 ( E 1 * E 1 z E 1 E 1 * z ) ( 1 1 | E 1 | 2 ) γ 2 | E 1 x | 2 1 2 γ ( | E 1 | 2 + 2 | E 2 | 2 3 ) ( | E 1 | 2 1 ) ,
L ˜ 2 = i 2 ( E 2 * E 2 z E 2 E 2 * z ) ( 1 1 | E 2 | 2 ) 1 2 | E 2 x | 2 1 2 ( 2 | E 1 | 2 + | E 2 | 2 3 ) ( | E 2 | 2 1 ) .
L 1 = 2 d x 1 d z [ A 1 B 1 + tan 1 ( B 1 A 1 ) ] 2 γ 3 B 1 2 D 2 B 1 2 ( B 1 2 + 2 B 2 2 ) 3 γ D ,
L 2 = 2 d x 2 d z [ A 2 B 2 + tan 1 ( B 2 A 2 ) ] 2 3 B 2 2 D 2 B 2 2 ( 2 B 1 2 + B 2 2 ) 3 D .
D 2 = B 1 2 ( B 1 2 + 2 B 2 2 ) γ 2 B 1 2 + γ B 2 2 + B 2 2 ( 2 B 1 2 + B 2 2 ) γ B 1 2 + B 2 2 ,
d x 1 d z = A 1 3 B 1 [ γ D + 2 ( B 1 2 + B 2 2 ) γ D + 2 B 2 2 D ] ,
d x 2 d z = A 2 3 B 2 [ D + 2 B 1 2 γ D + 2 ( B 1 2 + B 2 2 ) D ] .
γ 2 2 ψ x 2 + k ψ 1 γ ( | ψ | 2 + 2 | ϕ | 2 ) ψ = 0 ,
1 2 2 ϕ x 2 + k ϕ ( 2 | ψ | 2 + | ϕ | 2 ) ϕ = 0 ,

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