混合耦合非线性Schrödinger方程的Riemann-Hilbert方法及其孤子解

doi:10.52396/JUST-2021-0059

中国科学技术大学学报 ›› 2021, Vol. 51 ›› Issue (3): 196-201.DOI: 10.52396/JUST-2021-0059

混合耦合非线性Schrödinger方程的Riemann-Hilbert方法及其孤子解

胡贝贝^1,2, 张玲^1*, 方芳¹, 张宁³

1.滁州学院数学与金融学院,安徽滁州 239000;
2.浙江师范大学物理系,浙江金华 321004;
3.山东科技大学公共基础课教学部,山东泰安 271019

收稿日期:2021-03-01 修回日期:2021-03-20 出版日期:2021-03-31 发布日期:2021-11-16
通讯作者: * E-mail: originzhang@126.com

Riemann-Hilbert approach for a mixed coupled nonlinear Schrödinger equations and its soliton solutions

Hu Beibei^1,2, Zhang Ling^1*, Fang Fang¹, Zhang Ning³

1. School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, China;
2. Department of Physics, Zhejiang Normal University, Jinhua 321004, China;
3. Department of Basical Courses, Shandong University of Science and Technology, Taian 271019, China

Received:2021-03-01 Revised:2021-03-20 Online:2021-03-31 Published:2021-11-16
Contact: *E-mail: originzhang@126.com

摘要/Abstract

摘要： 研究了可积混合耦合的非线性Schrödinger(MCNLS)方程, 该方程可以用来描述双折射光纤中光脉冲的传播. 基于Riemann-Hilbert(RH)方法, 在构造的矩阵RH问题的跳跃矩阵为3×3单位矩阵时, 给出了MCNLS方程N-孤子解的显式表达式, 作为例子说明, 给出了1-孤子和2-孤子的显式表达式. 更一般地, 作为推广,还讨论了可积广义多分量NLS系统的线性谱问题.

关键词: Lax对, Riemann-Hilbert方法, 混合耦合非线性Schrödinger方程, 孤子解, 边界条件

Abstract: The integrable mixed coupled nonlinear Schrödinger (MCNLS) equations is studied, which describes the propagation of an optical pulse in a birefringent optical fiber. By the Riemann-Hilbert (RH) approach, the N-soliton solutions of the MCNLS equations can be expressed explicitly when the jump matrix of a constructed RH problem is a 3×3 unit matrix. As a special example, the expression of one soliton and two solitons are displayed explicitly. More generally, as a promotion, an integrable generalized multi-component NLS system with its linear spectral problem is discussed.

Key words: Lax pair, Riemann-Hilbert approach, mixed coupled nonlinear Schrödinger (MCNLS) equations, soliton solution, boundary conditions

中图分类号:

O175.29

胡贝贝, 张玲, 方芳, 张宁. 混合耦合非线性Schrödinger方程的Riemann-Hilbert方法及其孤子解[J]. 中国科学技术大学学报, 2021, 51(3): 196-201.

HU Beibei, ZHANG Ling, FANG Fang, ZHANG Ning. Riemann-Hilbert approach for a mixed coupled nonlinear Schrödinger equations and its soliton solutions[J]. Journal of University of Science and Technology of China, 2021, 51(3): 196-201.

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混合耦合非线性Schrödinger方程的Riemann-Hilbert方法及其孤子解

Riemann-Hilbert approach for a mixed coupled nonlinear Schrödinger equations and its soliton solutions

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