中国物理B ›› 2024, Vol. 33 ›› Issue (11): 110204-110204.doi: 10.1088/1674-1056/ad7e9e

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

Xin Zhao(赵鑫)1,†, Zhong Du(杜仲)2, Li-Jian Zhou(周立俭)1, Rong-Xiang Liu(刘荣香)1, and Xu-Hu Wang(王绪虎)1   

  1. 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
  • 收稿日期:2024-08-30 修回日期:2024-09-19 接受日期:2024-09-24 出版日期:2024-11-15 发布日期:2024-11-15
  • 基金资助:
    Project supported by the the Fundamental Research Funds for the Central Universities (Grant No. 2023MS163).

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

Xin Zhao(赵鑫)1,†, Zhong Du(杜仲)2, Li-Jian Zhou(周立俭)1, Rong-Xiang Liu(刘荣香)1, and Xu-Hu Wang(王绪虎)1   

  1. 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
  • Received:2024-08-30 Revised:2024-09-19 Accepted:2024-09-24 Online:2024-11-15 Published:2024-11-15
  • Contact: Xin Zhao E-mail:zhaoxin@qut.edu.cn
  • Supported by:
    Project supported by the the Fundamental Research Funds for the Central Universities (Grant No. 2023MS163).

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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 $N$th-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, $h_1(z)$, $p_1(z)$, $r_1(z)$, and $s_1(z)$ 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 $h_1(z)$, $p_1(z)$, $r_1(z)$, and $s_1(z)$, and the background wave depends on $g(z)$.

关键词: optical fiber, planar waveguide, Darboux transformation, bright soliton, breather

Abstract: 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 $N$th-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, $h_1(z)$, $p_1(z)$, $r_1(z)$, and $s_1(z)$ 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 $h_1(z)$, $p_1(z)$, $r_1(z)$, and $s_1(z)$, and the background wave depends on $g(z)$.

Key words: optical fiber, planar waveguide, Darboux transformation, bright soliton, breather

中图分类号:  (Partial differential equations)

  • 02.30.Jr
42.50.Md (Optical transient phenomena: quantum beats, photon echo, free-induction decay, dephasings and revivals, optical nutation, and self-induced transparency)