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Discrete Toda lattices and the Laplace method

  • V. L. VereschaginEmail author
Article
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Abstract

We apply the Laplace cascade method to systems of discrete equations of the form u i+1,j+1 = f(u i+1,j , u i,j+1, u i,j , u i,j−1), where u ij , i, j ∈ ℤ, is an element of a sequence of unknown vectors. We introduce the concept of a generalized Laplace invariant and the related property that the systems is “of the Liouville type.” We prove a series of statements about the correctness of the definition of the generalized invariant and its applicability for seeking solutions and integrals of the system. We give some examples of systems of the Liouville type.

Keywords

nonlinear discrete equation Laplace method Darboux integrability 

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Copyright information

© MAIK/Nauka 2009

Authors and Affiliations

  1. 1.Institute of Mathematics, Ufa Science CenterRASUfaRussia

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