Discrete analogues of the Liouville equation
solv-int
2014-08-27 v1 Exactly Solvable and Integrable Systems
Abstract
The notion of Laplace invariants is transferred to the lattices and discrete equations which are difference analogs of hyperbolic PDE's with two independent variables. The sequence of Laplace invariants satisfy the discrete analog of twodimensional Toda lattice. The terminating of this sequence by zeroes is proved to be the necessary condition for existence of the integrals of the equation under consideration. The formulae are presented for the higher symmetries of the equations possessing integrals. The general theory is illustrated by examples of difference analogs of Liouville equation.
Keywords
Cite
@article{arxiv.solv-int/9902016,
title = {Discrete analogues of the Liouville equation},
author = {V. E. Adler and S. Ya. Startsev},
journal= {arXiv preprint arXiv:solv-int/9902016},
year = {2014}
}
Comments
LaTeX, 15 pages, submitted to Teor. i Mat. Fiz