Riemann-Hilbert approach and N-soliton solutions for the three-component coupled Hirota equations

TL;DR

This paper employs the Riemann-Hilbert approach to derive N-soliton solutions for the integrable three-component coupled Hirota equations, analyzing soliton interactions and presenting new dynamic phenomena.

Contribution

It introduces a Riemann-Hilbert framework for the three-component coupled Hirota equations and constructs explicit N-soliton solutions, revealing novel soliton collision behaviors.

Findings

Derived explicit N-soliton solutions.

Analyzed collision dynamics and control of soliton interactions.

Discovered new phenomena in soliton collision behaviors.

Abstract

In this work, we consider an integrable three-component coupled Hirota (tcCH) equations in detail via the Riemann-Hilbert (RH) approach. We present some properties of the spectral problems of the tcCH equations with $4\times4$ the Lax pair. Moreover, the RH problem of the equations is established via analyzing the analyticity of the spectrum problem. By studying the symmetry of the spectral problem, we get the spatiotemporal evolution of scattering data. Finally, the $N$-soliton solution is derived by solving the RH problem with reflectionless case. According to the resulting $N$-soliton solution, the influences of each parameters on collision dynamic behaviors between solitons are discussed, and the method of how to control the interactions are suggested by some graphic analysis. In addition, some new phenomenon for soliton collision is presented including localized structures and dynamic behaviors of one- and two- soliton solutions, which can help enrich the nonlinear dynamics of the $N$-component nonlinear Schr\"{o}dinger type equations.