Interactions and asymptotic analysis of N-soliton solutions for the n-component generalized higher-order Sasa-Satsuma equations.

Abstract

In this paper, we systematically study the N-solitons and asymptotic analysis of the integrable n-component third-fifth-order Sasa-Satsuma equations. We conduct the spectral analysis on the (n+2)-order matrix Lax pair to formulate a Riemann-Hilbert (RH) problem, which is used to generate the N-soliton solutions via the determinants. Moreover, we visually represent the interaction dynamics of multi-soliton solutions and analyze their asymptotic behaviors. Finally, we present the higher-order N-soliton solutions by dealing with the RH problem with higher-order zeros. These results will be useful to further analyze the multi-soliton structures and design the related physical experiments.