Multi-Soliton Solutions for the Nonlocal Kundu-Nonlinear Schrödinger Equation with Step-Like Initial Data

Abstract

We investigate the multi-soliton solutions for the Cauchy problem of the nonlocal Kundu-nonlinear Schrödinger (NK-NLS) equation with step-like initial data. We first perform the spectral analysis on the Lax pair of the NK-NLS equation, and then establish the Riemann-Hilbert (RH) problem of the equation based on the analytic, symmetric and asymptotic properties of Jost solutions and spectral functions. Because of the influence of step-like initial value, we need to consider the singularity condition of the RH problem at the origin, and this singularity condition can be converted to a residue condition. Further, the multi-soliton solutions of the NK-NLS equation are obtained in terms of the corresponding RH problem.