The Fokas Method for the Broer-Kaup System on the Half-Line

Abstract

AbstractWe analyze the Broer-Kaup system posed on the half-line by using the unified transform method, also known as the Fokas method. We derive the formal representation of the solution for the Broer-Kaup system in terms of the solution of the matrix Riemann-Hilbert problem formulated in the complex plane of the spectral parameter. The jump matrix is uniquely defined by the spectral functions that satisfy a certain relation, called the global relation involving the initial and boundary values. Furthermore, the spectral functions constructed from the initial values and the boundary values are investigated, plus their associated Riemann-Hilbert problems as the inverse problems.