Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (1): 101-122.

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Simple-Pole and Double-Pole Solutions for the Mixed Chen-Lee-Liu Derivative Nonlinear Schrödinger Equation with Nonzero Boundary Conditions

Chunjiang Wang1,*(),Jian Zhang2()   

  1. 1School of Mathematical Sciences, Sichuan Normal University, Chengdu 610100
    2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731
  • Received:2021-12-29 Revised:2022-08-09 Online:2023-02-26 Published:2023-03-07
  • Supported by:
    The NSFC(11871138)


This paper is concerned with simple-pole and double-pole solutions for the mixed Chen-Lee-Liu derivative nonlinear Schr?dinger equation with non-zero boundary conditions at infinity. By solving a direct scattering problem, the Jost eigenfunctions and scattering matrix are given, their symmetries and asymptotic behaviors are also presented. Then the inverse scattering problems are solved in terms of the matrix Riemann-Hilbert method. In addition, the trace formulae for analytic scattering coefficients and theta conditions are derived. Finally, the explicit formulae of double-pole solutions for the equation are obtained.

Key words: Nonlinear Schr?dinger equation, Non-zero boundary conditions, Inverse scattering, Riemann-Hilbert problem, Double-pole solution

CLC Number: 

  • O175