Spectral and soliton structures for the four-component Kaup–Newell type negative flow equation

Abstract

Based on the spectral analysis of Lax pairs and the inverse scattering method, we construct a matrix Riemann–Hilbert problem of the four-component Kaup–Newell type negative flow equation associated with a 4 × 4 matrix spectral problem and investigate the evolution of scattering data. Then N-soliton formulas of the four-component Kaup–Newell type negative flow equation are obtained by solving the irregular Riemann–Hilbert problem in the reflectionless case. As an application, the one-soliton solutions and the two-soliton solutions of the four-component Kaup–Newell type negative flow equation are given explicitly. In addition, the interaction dynamics of the soliton solutions are analyzed and illustrated.