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 functions s(k) and S(k), which are determined by the initial values and boundary values at x=0, respectively. Some of these boundary values are unknown; however, using the fact that these specific functions satisfy a certain global relation, the unknown boundary values can be expressed in terms of the given initial and boundary data.
Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9.figshare.c.3577001.
- Received July 25, 2016.
- Accepted November 2, 2016.
- © 2016 The Author(s)
Published by the Royal Society. All rights reserved.