title: The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method.
abstract: In this paper, we implement the Fokas method to study initial-boundary value problems of the mixed coupled nonlinear Schrödinger equation formulated on the half-line with Lax pairs involving 3×3 matrices. The solution can be written in terms of the solution to a 3×3 Riemann-Hilbert problem. The relevant jump matrices are explicitly expressed in terms of the matrix-value spectral functionss(k) andS(k), which are determined by the initial values and boundary values atx=0, respectively. Some of these boundary values are unknown; however, using the fact that these specific functions satisfy a certainglobal relation, the unknown boundary values can be expressed in terms of the given initial and boundary data.
authors.affiliation: Department of Mathematics , China University of Mining and Technology , Xuzhou 221116, People's Republic of China.
authors.forename: Shou-Fu
authors.identifier: 0000-0003-0888-777X
authors.initials: SF
authors.lastname: Tian
keywords: Riemann–Hilbert problem; initial-boundary value problem; mixed coupled nonlinear Schrödinger equation