This article is cited in 6 papers

Riemann–Hilbert problem for the Kundu-type nonlinear Schrödinger equation with $N$ distinct arbitrary-order poles

Zi-Yi Wang, Shou-Fu Tian, Xiao-Fan Zhang

School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou, China

Abstract: We use the Riemann–Hilbert (RH) method to study the Kundu-type nonlinear Schrödinger (Kundu–NLS) equation with a zero boundary condition in the case where the scattering coefficient has $N$ distinct arbitrary-order poles. We perform a spectral analysis of the Lax pair and consider the asymptotic property, symmetry, and analyticity of the Jost solution. Based on these results, we formulate the RH problem whose solution allows solving the considered Kundu–NLS equation. In addition, using graphic analysis, we study the characteristics of soliton solutions of some particular cases of the problem with $N$ distinct arbitrary-order poles.

Keywords: Kundu–nonlinear Schrödinger equation, zero boundary condition, Riemann–Hilbert problem, arbitrary-order pole, scattering coefficient, soliton solution.

Received: 26.11.2020
Revised: 25.12.2020

DOI: 10.4213/tmf10015

 English version: Theoretical and Mathematical Physics, 2021, 207:1, 415–433

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