Lax pair and vector solitons for a variable-coefficient coherently-coupled nonlinear Schrödinger system in the nonlinear birefringent optical fiber

Jun Chai, Bo Tian, Han-Peng Chai and Yu-Qiang Yuan

Journal of Electromagnetic Waves and Applications, 2017, vol. 31, issue 14, 1363-1375

Abstract: Nowadays, with respect to the nonlinear birefringent optical fibers, efforts have been put into investigating the coupled nonlinear Schrödinger (NLS) systems. In this paper, symbolic computation on a variable-coefficient coherently-coupled NLS system with the alternate signs of nonlinearities is performed. Under a variable-coefficient constraint Ω(t)2=[lnγ(t)]t2-[lnγ(t)]tt$ \Omega (t)^{2}=[\ln \gamma (t)]_{t}^{2}-[\ln \gamma (t)]_{tt} $, the system is shown to be integrable in the Lax sense with a Lax pair constructed, where t is the normalized time, γ(t)$ \gamma (t) $ is the strength of the four wave mixing terms, and Ω(t)2$ \Omega (t)^{2} $ is the strength of the anti-trapping parabolic potential. With an auxiliary function, bilinear forms, vector one- and two-soliton solutions are obtained. Figures are displayed to help us study the vector solitons: When γ(t)$ \gamma (t) $ is a constant, vector soliton propagates stably with the amplitude and velocity unvarying (vector soliton’s amplitude changes with the change of that constant, while its velocity can not be affected by that constant); When γ(t)$ \gamma (t) $ is a t-varying function, i.e. Ω(t)2≠0$ \Omega (t)^{2}\ne 0 $, amplitude and velocity of the vector soliton both vary with t increasing, while Ω(t)2$ \Omega (t)^{2} $ affects the vector soliton’s amplitude and velocity. With the different γ(t)$ \gamma (t) $ or Ω(t)2$ \Omega (t)^{2} $, interactions between the amplitude- and velocity-unvarying vector two solitons and those between the amplitude- and velocity-varying vector two solitons are displayed, respectively. By virtue of the system and its complex-conjugate system, conservation laws for the vector solitons, including the total energy and momentum, are constructed.

Date: 2017
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DOI: 10.1080/09205071.2017.1348994

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