AI Article Synopsis
- The paper uses the Fokas method to analyze initial-boundary value problems for a mixed coupled nonlinear Schrödinger equation on a half-line.
- The solutions are linked to a 3×3 Riemann-Hilbert problem, with jump matrices defined by matrix-valued spectral functions determined by initial and boundary conditions.
- The study reveals that even with some unknown boundary values, they can be determined using the properties of the spectral functions based on known initial and boundary data.
Article 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 () and (), which are determined by the initial values and boundary values at =0, respectively. Some of these boundary values are unknown; however, using the fact that these specific functions satisfy a certain , the unknown boundary values can be expressed in terms of the given initial and boundary data.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5134312 | PMC |
| http://dx.doi.org/10.1098/rspa.2016.0588 | DOI Listing |
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