Integrable lattice equations and their growth properties
Mathematical Physics
2013-07-10 v1 math.MP
Abstract
In this paper we investigate the integrability of two-dimensional partial difference equations using the newly developed techniques of study of the degree of the iterates. We show that while for generic, nonintegrable equations, the degree grows exponentially fast, for integrable lattice equations the degree growth is polynomial. The growth criterion is used in order to obtain the integrable deautonomisations of the equations examined. In the case of linearisable lattice equations we show that the degree growth is slower than in the case of equations integrable through Inverse Scattering Transform techniques.
Cite
@article{arxiv.0709.3095,
title = {Integrable lattice equations and their growth properties},
author = {Sébastien Tremblay and Basile Grammaticos and Alfred Ramani},
journal= {arXiv preprint arXiv:0709.3095},
year = {2013}
}