N-soliton solutions for the novel Kundu-nonlinear Schrödinger equation and Riemann–Hilbert approach

Abstract

This paper investigates the novel Kundu-nonlinear Schrödinger equation (nKundu-NLS) with zero boundary conditions by applying the inverse scattering method. A suitable Riemann–Hilbert problem (RHP) is formulated and solved by the Laurent expansion method. Through the Laurent series, the paper obtains the solutions of the RHP for different cases of the reflection coefficient, such as single and multiple poles. The paper demonstrates the effectiveness and generality of the inverse scattering method for solving the nKundu-NLS.