dorsal/arxiv
View SchemaDiscrete analogues of the Liouville equation
| Authors | V. E. Adler, S. Ya. Startsev |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9902016 |
| URL | https://arxiv.org/abs/solv-int/9902016 |
| DOI | 10.1007/BF02557219 |
| Journal | Theoretical and Mathematical Physics 1999, Volume 121, Issue 2, pp 1484-1495 |
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.
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"abstract": "The notion of Laplace invariants is transferred to the lattices and discrete\nequations which are difference analogs of hyperbolic PDE\u0027s with two independent\nvariables. The sequence of Laplace invariants satisfy the discrete analog of\ntwodimensional Toda lattice. The terminating of this sequence by zeroes is\nproved to be the necessary condition for existence of the integrals of the\nequation under consideration. The formulae are presented for the higher\nsymmetries of the equations possessing integrals. The general theory is\nillustrated by examples of difference analogs of Liouville equation.",
"arxiv_id": "solv-int/9902016",
"authors": [
"V. E. Adler",
"S. Ya. Startsev"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1007/BF02557219",
"journal_ref": "Theoretical and Mathematical Physics 1999, Volume 121, Issue 2, pp\n 1484-1495",
"title": "Discrete analogues of the Liouville equation",
"url": "https://arxiv.org/abs/solv-int/9902016"
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