Asymptotic analysis on bright solitons and breather solutions of a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide
1 College of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China; 2 Department of Mathematics and Physics, and Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China
Abstract We study a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide. We obtain the Lax pair and -fold Darboux transformation (DT) with 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 -soliton solutions, and the first-, second-, and th-order breather solutions based on the -fold DT. We conclude that the velocities of the bright solitons are influenced by the distributed gain function, , and variable coefficients in equation, , , , and via the asymptotic analysis, where 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 , , , and , and the background wave depends on .
Xin Zhao(赵鑫), Zhong Du(杜仲), Li-Jian Zhou(周立俭), Rong-Xiang Liu(刘荣香), and Xu-Hu Wang(王绪虎) Asymptotic analysis on bright solitons and breather solutions of a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide 2024 Chin. Phys. B 33 110204
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