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The mixed coupled nonlinear Schrodinger 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 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.

SUBMITTER: Tian SF

PROVIDER: S-EPMC5134312 | biostudies-literature | 2016 Nov

REPOSITORIES: biostudies-literature

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The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method.

Tian Shou-Fu SF

Proceedings. Mathematical, physical, and engineering sciences 20161101 2195

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 ...[more]

PMID: 27956881

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