Initial-boundary value problems associated with the Ablowitz-Ladik system
Exactly Solvable and Integrable Systems
2018-03-26 v4
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 Schr\"{o}dinger 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.
Cite
@article{arxiv.1703.01687,
title = {Initial-boundary value problems associated with the Ablowitz-Ladik system},
author = {Baoqiang Xia and A. S. Fokas},
journal= {arXiv preprint arXiv:1703.01687},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1703.01689