# A Riemann-Hilbert Approach to the Complex Sharma-Tasso-Olver Equation on the Half Line

## TL;DR

This paper applies the Fokas method to analyze the complex Sharma-Tasso-Olver equation on a half line, representing it through a matrix Riemann-Hilbert problem in the spectral plane.

## Contribution

It introduces a Riemann-Hilbert problem formulation for the complex Sharma-Tasso-Olver equation using the Fokas method, providing a new analytical approach.

## Key findings

- Representation of the cSTO equation via a matrix RHP
- Application of the Fokas method to boundary value problems
- Framework for solving cSTO on the half line

## Abstract

In this paper, we use the Fokas method to analyze the complex Sharma-Tasso-Olver(cSTO) equation on the half line. We show that it can be represented in terms of the solution of a matrix RHP formulated in the plane of the complex spectral parameter {\lambda}.