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Theoretical and Mathematical Physics

, Volume 121, Issue 2, pp 1484–1495 | Cite as

Discrete analogues of the Liouville equation

  • V. E. Adler
  • S. Ya. Startsev
Article

Abstract

The notion of Laplace invariants is generalized to lattices and discrete equations that are difference analogues of hyperbolic partial differential equations with two independent variables. The sequence of Laplace invariants satisfies the discrete analogue of the two-dimensional Toda lattice. We prove that terminating this sequence by zeros is a necessary condition for the existence of integrals of the equation under consideration. We present formulas for the higher symmetries of equations possessing such integrals. We give examples of difference analogues of the Liouville equation.

Keywords

Dynamic Variable Liouville Equation Continuous Case Discrete Case Discrete Analogue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • V. E. Adler
    • 1
  • S. Ya. Startsev
    • 1
  1. 1.Institute for Mathematics and Computation Center, Ufa Science CenterRASUfaRussia

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