具有非零边界条件的混合 Chen-Lee-Liu 导数非线性薛定谔方程的单极解和双极解

Abstract

Abstract:

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

Wang Chunjiang, Zhang Jian. Simple-Pole and Double-Pole Solutions for the Mixed Chen-Lee-Liu Derivative Nonlinear Schrödinger Equation with Nonzero Boundary Conditions[J].Acta mathematica scientia,Series A, 2023, 43(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

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