Discrete analogues of the Liouville equation

Details Discrete analogues of the Liouville equation Discrete analogues of the Liouville equation

1999-02-23

arxiv.org/abs/solv-int/9902016v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX, 15 pages, submitted to Teor. i Mat. Fiz

Scientific paper

10.1007/BF02557219

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.

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