The soliton solutions for the higher‐order nonlinear Schrödinger equation with nonzero boundary conditions: Riemann–Hilbert method

Abstract

This paper explores the Riemann–Hilbert method for deriving exact N‐soliton solutions of the sixth‐order nonlinear Schrödinger (6th‐NLS) equation with nonzero boundary condition. The analytical process comprises three fundamental steps. First, transformations are used to simplify the nonzero boundaries. Next, the inverse scattering method establishes a crucial link between the solutions of the 6th‐NLS equation and the corresponding Riemann–Hilbert problem. Finally, this Riemann–Hilbert problem is systematically solved. Additionally, selected parameter values in the solutions generate graphical representations, vividly illustrating the solutions to the 6th‐NLS equation.