Asymptotic analysis on bright solitons and breather solutions of a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide

被引:0
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作者
Zhao, Xin [1 ]
Du, Zhong [2 ]
Zhou, Li-Jian [1 ]
Liu, Rong-Xiang [1 ]
Wang, Xu-Hu [1 ]
机构
[1] College of Information and Control Engineering, Qingdao University of Technology, Qingdao,266520, China
[2] Department of Mathematics and Physics, Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding,071003, China
关键词
Asymptotic analysis - Nonlinear equations - Nonlinear optics - Optical depth - Optical fibers - Optical transitions - Schrodinger equation - Waveguide transformers - Z transforms;
D O I
10.1088/1674-1056/ad7e9e
中图分类号
学科分类号
摘要
We study a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide. We obtain the Lax pair and N-fold Darboux transformation (DT) with N being a positive integer. Based on Lax pair obtained by us, we derive the infinitely-many conservation laws. We give the bright one-, two-, and N-soliton solutions, and the first-, second-, and Nth-order breather solutions based on the N-fold DT. We conclude that the velocities of the bright solitons are influenced by the distributed gain function, g(z), and variable coefficients in equation, h1(z), p1(z), r1(z), and s1(z) via the asymptotic analysis, where z represents the propagation variable or spatial coordinate. We also graphically observe that: the velocities of the first- and second-order breathers will be affected by h1(z), p1(z), r1(z), and s1(z), and the background wave depends on g(z). © 2024 Chinese Physical Society and IOP Publishing Ltd.
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