数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (1): 113-126.doi: 10.1007/s10473-020-0108-x

• 论文 • 上一篇    下一篇

N-SOLITON SOLUTION OF THE KUNDU-TYPE EQUATION VIA RIEMANN-HILBERT APPROACH

温丽丽1, 张宁2, 范恩贵1   

  1. 1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
    2. Department of Basic Courses, Shandong University of Science and Technology, Taian 266510, China
  • 收稿日期:2018-12-11 修回日期:2019-02-09 出版日期:2020-02-25 发布日期:2020-04-14
  • 通讯作者: Engui FAN E-mail:faneg@fudan.edu.cn
  • 基金资助:
    This work was supported by the National Science Foundation of China (11671095, 51879045, 11805114).

N-SOLITON SOLUTION OF THE KUNDU-TYPE EQUATION VIA RIEMANN-HILBERT APPROACH

Lili WEN1, Ning ZHANG2, Engui FAN1   

  1. 1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
    2. Department of Basic Courses, Shandong University of Science and Technology, Taian 266510, China
  • Received:2018-12-11 Revised:2019-02-09 Online:2020-02-25 Published:2020-04-14
  • Contact: Engui FAN E-mail:faneg@fudan.edu.cn
  • Supported by:
    This work was supported by the National Science Foundation of China (11671095, 51879045, 11805114).

摘要: In this article, we focus on investigating the Kundu-type equation with zero boundary condition at infinity. Based on the analytical and symmetric properties of eigenfunctions and spectral matrix of its Lax pair, a Riemann-Hilbert problem for the initial value problem of the Kundu-type equation is constructed. Further through solving the regular and nonregular Riemann-Hilbert problem, a kind of general N-soliton solution of the Kundu-type equation are presented. As special cases of this result, the N-soliton solution of the Kaup-Newell equation, Chen-Lee-Liu equation, and Gerjikov-Ivanov equation can be obtained respectively by choosing different parameters.

关键词: the Kundu-type equation, Lax pair, Riemann-Hilbert problem, soliton solution

Abstract: In this article, we focus on investigating the Kundu-type equation with zero boundary condition at infinity. Based on the analytical and symmetric properties of eigenfunctions and spectral matrix of its Lax pair, a Riemann-Hilbert problem for the initial value problem of the Kundu-type equation is constructed. Further through solving the regular and nonregular Riemann-Hilbert problem, a kind of general N-soliton solution of the Kundu-type equation are presented. As special cases of this result, the N-soliton solution of the Kaup-Newell equation, Chen-Lee-Liu equation, and Gerjikov-Ivanov equation can be obtained respectively by choosing different parameters.

Key words: the Kundu-type equation, Lax pair, Riemann-Hilbert problem, soliton solution

中图分类号: 

  • 35Q51