We study interaction of different-polarization single-component vector solitons of the envelope function in anisotropic media within the framework of the system of two coupled third-order nonlinear Schrödinger equations which allow for the third-order linear dispersion, nonlinear dispersion, nonlinear cross-phase modulation, and cross-nonlinear dispersion. The regimes of mutual reflection, passage, and asymptotic approach of the solitons are obtained. It is shown that the character of interaction of such solitons is determined by the initial relationship of their amplitudes and phases. The stationary mutual locations of interacting solitons and their coupled, the so-called breather states are discussed. The roles of the cubic nonlinearity, cubic cross-nonlinearity, and cross-nonlinear dispersion during interaction of solitons are studied.
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References
Y. Yang, Solitons in Field Theory and Nonlinear Analysis, Springer, New York (2001).
L. A. Dickey, Soliton Equation and Hamiltonian Systems, World Scientific, New York (2005).
Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals, Academic Press, San Diego (2003).
G. P. Agrawal, Fiber Optic Communication Systems, Wiley, Hoboken, N.J. (2002).
J. R. Oliviera and M. A. Moura, Phys. Rev. E, 57, 4751 (1998).
Y. J. Kodama, Stat. Phys., 39, 597 (1985).
C. E. Zaspel, Phys. Rev. Lett., 82, 723 (1999).
B. Hong and D. Lu, Int. J. Nonlin. Sci., 7, 360 (2009).
V. I. Karpman, Eur. Phys. J. B, 39, 341 (2004).
E. M. Gromov and V. I. Talanov, JETP, 83, No. 1, 73 (1996).
E. M. Gromov and V. I. Talanov, Chaos, 10, 551 (2000).
E. M. Gromov, L. V. Piskunova, and V. V. Tyutin, Phys. Lett. A, 256, 153 (1999).
N. L. Tsitsas, N. Rompolis, I. Kourakis, et al., Phys. Rev. E., 79, 037601 (2009).
V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP, 34, No. 1, 62 (1972).
A. Hasegava and F. Tappert, Appl. Phys. Lett., 23, 142 (1973).
S. V. Manakov, Sov. Phys. JETP, 38, No. 2, 248 (1974).
J. Satsuma and N. Yajima, Suppl. Progress Theor. Phys., 55, 284 (1974).
S. N. Vlasov and V. I. Talanov, Self-Focusing of Waves [in Russian], Inst. Appl. Phys., Nizhny Novgorod (1997).
Su Ming-Yang, Phys. Fluids, 12, 25 (1982).
E. M. Gromov and V. I. Talanov, in: Int. School in Nonlinear Science, Nonlinear Waves, Synchronization, and Pattern, Nizhny Novgorod State Univ., Nizhny Novgorod (1995), p. 23.
G. P. Agrawal, Nonlinear Fiber Optics, Academic Press, San Diego (1989).
D. N. Christodoulides and R. I. Joseph, Electron. Lett., 20, 659 (1984).
J. Kim, ETRI J., 23, 9 (2001).
F. Lu, W. H. Lin, W. H. Knox, and G. P. Agrawal, Phys. Rev. Lett., 93, 183901 (2004).
E. M. Gromov, V. V. Tyutin, and D. E. Vorontzov, Phys. Lett. A, 287, 233 (2001).
A. P. Fordy and P. P. Kullish, Commun. Math. Phys., 89, 427 (1983).
C. R. Menyuk, J. Opt. Soc. Am. B, 5, 392 (1988).
V. I. Nayanov, Multi-Field Solitons [in Russian], Fizmztlit, Moscow (2006).
N. V. Aseeva, E. M. Gromov, and V. V. Tyutin, Phys. Lett. A, 376, 718 (2012).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 55, No. 3, pp. 203–217, March 2012.
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Aseeva, N.V., Gromov, E.M. & Tyutin, V.V. Interaction of short single-component vector solitons. Radiophys Quantum El 55, 184–197 (2012). https://doi.org/10.1007/s11141-012-9359-z
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DOI: https://doi.org/10.1007/s11141-012-9359-z