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

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 , the system is shown to be integrable in the Lax sense with a Lax pair constructed, where t is the normalized time, is the strength of the four wave mixing terms, and 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 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 is a t-varying function, i.e. , amplitude and velocity of the vector soliton both vary with t increasing, while affects the vector soliton’s amplitude and velocity. With the different or , 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.

Keywords:

• Nonlinear birefringent optical fibers
• variable-coefficient coherently-coupled nonlinear Schrödinger system
• Lax pair
• vector solitons
• conservation laws

Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the National Natural Science Foundation of China [grant number 11272023], [grant number 11471050]; the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications); the Fundamental Research Funds for the Central Universities of China [grant number 2011BUPTYB02].