On an integrable discretization of the modified Korteweg-de Vries equation
solv-int
2016-09-08 v1 Exactly Solvable and Integrable Systems
Abstract
We find time discretizations for the two ''second flows'' of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one-field reduction and serve therefore as valid space-time discretizations of the modified Korteweg-de Vries equation. We expect the performance of these discretizations to be much better then that of the Taha-Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well as the solution of an initial value problem in terms of matrix factorizations.
Cite
@article{arxiv.solv-int/9702003,
title = {On an integrable discretization of the modified Korteweg-de Vries equation},
author = {Yuri B. Suris},
journal= {arXiv preprint arXiv:solv-int/9702003},
year = {2016}
}
Comments
23 pages, LaTeX