The coupled modified nonlinear Schr\"{o}dinger equations on the half-line via the Fokas method

Abstract

Coupled modified nonlinear Schr\"{o}dinger(CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. In this paper, we use the Fokas method to analyze the initial-boundary value problem for the CMNLS equations on the half-line. Assume that the solution u(x,t) and v(x,t) of CMNLS 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}.