# The coupled modified nonlinear Schr\"{o}dinger equations on the half-line via the Fokas method

## TL;DR

This paper applies the Fokas method to analyze the initial-boundary value problem for coupled modified nonlinear Schrödinger equations on the half-line, expressing solutions via a matrix Riemann-Hilbert problem.

## Contribution

It introduces a novel application of the Fokas method to coupled CMNLS equations on the half-line, deriving a Riemann-Hilbert problem formulation for solutions.

## Key findings

- Solution expressed in terms of a matrix Riemann-Hilbert problem
- Provides a framework for analyzing CMNLS equations on the half-line
- Establishes existence and uniqueness assumptions for solutions

## Abstract

Coupled modified nonlinear Schr\"{o}dinger(CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. In this paper, we use the Fokas method to analyze the initial-boundary value problem for the CMNLS equations on the half-line. Assume that the solution u(x,t) and v(x,t) of CMNLS equations are exists, and we show that it can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter {\lambda}.