# Constructing Riemann-Hilbert problem and multi-soliton solutions for the N-coupled Hirota equations in an optical fiber

## TL;DR

This paper develops a Riemann-Hilbert problem approach to derive multi-soliton solutions for N-coupled Hirota equations in optical fibers, advancing analytical methods for complex nonlinear wave systems.

## Contribution

It introduces a new matrix Riemann-Hilbert formulation for N-coupled Hirota equations and explicitly constructs multi-soliton solutions under no reflection conditions.

## Key findings

- Explicit multi-soliton solutions derived
- Riemann-Hilbert problem formulated on the real axis
- Analytical framework applicable to optical fiber models

## Abstract

This paper focuses on investigation of the N-coupled Hirota equations arising in an optical fiber. Starting from analyzing the spectral problem, a kind of matrix Riemann-Hilbert problem is formulated strictly on the real axis. Then based on the resulting matrix Riemann-Hilbert problem under the constraint of no reflection, multi-soliton solutions to the N-coupled Hirota equations are presented explicitly.