Lax Pair, Improved \(\varGamma \)-Riccati Bäcklund Transformation and Soliton-Like Solutions to Variable-Coefficient Higher-Order Nonlinear Schrödinger Equation in Optical Fibers
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In this paper, the higher-order nonlinear Schrödinger equation with variable-coefficient for the propagation of femtosecond pulses in optical fibers is analytically investigated. Lax pair is constructed via the Ablowitz-Kaup-Newell-Segur system, an infinite number of conservation laws are derived based on the Lax pair. Introducing an auxiliary function, an improved \(\varGamma \)-Riccati Bäcklund transformation is presented, which can generate successively nonlinear superposition formula. Moreover, one and two soliton-like solutions are obtained.
KeywordsVariable-coefficient higher-order nonlinear Schrödinger equation Optical fiber Conservation law Improved \(\varGamma \)-Riccati Bäcklund transformation Soliton-like solution
We would like to thank the Editor and Reviewers for their timely and valuable comments. We also express sincere thanks to J.Y. Wang and W.X. Zheng for their valuable discussions and helpful advices. This work has been supported by the National Natural Science Foundation of China under Grant No. 61471406.
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