Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256292 | Physica D: Nonlinear Phenomena | 2018 | 58 Pages |
Abstract
We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Baoqiang Xia, A.S. Fokas,