On integrability test for ultradiscrete equations
solv-int
2007-05-23 v1 Exactly Solvable and Integrable Systems
Abstract
We consider an integrability test for ultradiscrete equations based on the singularity confinement analysis for discrete equations. We show how singularity pattern of the test is transformed into that of ultradiscrete equation. The ultradiscrete solution pattern can be interpreted as a perturbed solution. We can also check an integrability of a given equation by a perturbation growth of a solution, namely Lyapunov exponent. Therefore, singularity confinement test and Lyapunov exponent are related each other in ultradiscrete equations and we propose an integrability test from this point of view.
Cite
@article{arxiv.solv-int/9903012,
title = {On integrability test for ultradiscrete equations},
author = {Daisuke Takahashi and Kenji Kajiwara},
journal= {arXiv preprint arXiv:solv-int/9903012},
year = {2007}
}
Comments
10 pages including 5 figures