Integrability of Differential-Difference Equations with Discrete Kinks
Exactly Solvable and Integrable Systems
2015-05-20 v1 Mathematical Physics
math.MP
Pattern Formation and Solitons
Abstract
In this article we discuss a series of models introduced by Barashenkov, Oxtoby and Pelinovsky to describe some discrete approximations to the \phi^4 theory which preserve travelling kink solutions. We show, by applying the multiple scale test that they have some integrability properties as they pass the A_1 and A_2 conditions. However they are not integrable as they fail the A_3 conditions.
Keywords
Cite
@article{arxiv.1011.0068,
title = {Integrability of Differential-Difference Equations with Discrete Kinks},
author = {C. Scimiterna and D. Levi},
journal= {arXiv preprint arXiv:1011.0068},
year = {2015}
}
Comments
submitted to the Proceedings of the workshop "Nonlinear Physics: Theory and Experiment.VI" in a special issue di Theoretical and Mathematical Physics