On integrability test for ultradiscrete equations

Details On integrability test for ultradiscrete equations On integrability test for ultradiscrete equations

1999-03-15

arxiv.org/abs/solv-int/9903012v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages including 5 figures

Scientific paper

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.

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