The initial-boundary value problems for the coupled derivative nonlinear Schrödinger equations on the half-line

Abstract

The unified transform method is used to analyze the initial-boundary value problem for the coupled derivative nonlinear Schrödinger(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 $\lambda$.

arXiv admin note: substantial text overlap with arXiv:1704.03623, arXiv:1712.06449, arXiv:1711.03861