# The initial-boundary value problems for the coupled derivative nonlinear Schr\"odinger equations on the half-line

## TL;DR

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

## Contribution

It introduces a novel approach to solving CDNLS equations on the half-line using the unified transform method and Riemann-Hilbert problem formulation.

## Key findings

- Solution expressed in terms of a unique matrix Riemann-Hilbert problem.
- Provides a framework for analyzing initial-boundary value problems for CDNLS.
- Assumes existence of solutions to formulate the problem.

## Abstract

The unified transform method is used to analyze the initial-boundary value problem for the coupled derivative nonlinear Schr\"odinger(CDNLS) equations on the half-line. In this paper, we assume that the solution $u(x,t)$ and $v(x,t)$ of CDNLS 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 $\lambda$.