Riemann-Hilbert method and soliton solutions in the system of two-component Hirota equations

TL;DR

This paper derives explicit multi-soliton solutions for the integrable two-component Hirota equations using the Riemann-Hilbert method, providing insights into pulse propagation in coupled optical fibers with higher-order effects.

Contribution

It introduces a novel application of the Riemann-Hilbert method to obtain general N-soliton solutions for the two-component Hirota equations, a previously unaddressed integrable system.

Findings

Explicit one- and two-soliton solutions provided.

General N-soliton solutions derived via RH method.

Demonstrates integrability and solution structure of the system.

Abstract

In this letter we examine the two-component Hirota (TH) equations which describes the pulse propagation in a coupled fiber with higher-order dispersion and self-steepening. As the TH equations is a complete integrable system, which admits a $3\times 3$ Ablowitz-Kaup-Newell-Segu(AKNS)-type Lax pair, we obtain the general N-soliton solutions of the TH equations via the Riemann-Hilbert(RH) method when the jump matrix of a specific RH problem is a $3\times3$ unit matrix. As an example, the expression of one- and two-soliton are displayed explicitly.