A Riemann–Hilbert Approach to Complex Sharma–Tasso–Olver Equation on Half Line**Supported by National Natural Science Foundation of China under Grant Nos. 11271008 and 61072147

Abstract

In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma–Tasso–Olver (cSTO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann–Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions and , which depending on initial data and boundary data , , . These spectral functions are not independent, they satisfy a global relation.