Asymptotic diagonalization of the Discrete Lax pair around singularities and conservation laws for dynamical systems

Abstract

A method of the formal diagonalization of the discrete linear operator with a parameter is studied. In the case when the operator provides a Lax operator for a nonlinear quad system the formal diagonalization method allows one to describe effectively conservation laws and generalized symmetries for this system. Asymptotic representation of the Lax operators eigenfunctions are constructed and infinite series of conservation laws are described for the quad system connected with $A_3^{(1)}$ affine Lie algebra, for the modified discrete Boussinesq system and for the discrete Tzitzeica equation. For a newly found multiquadratic discrete model conservation laws and several generalized symmetries are presented.

32 pages

References in corpus (5)

• Boussinesq-like multi-component lattice equations and multi-dimensional consistency
• On a discrete analog of the Tzitzeica equation
• Discretisations of constrained KP hierarchies
• Integrable Discrete Nonautonomous Quad-equations as Bäcklund Auto-transformations for Known Volterra and Toda Type Semidiscrete Equations
• Affine Lie algebras, Lax pairs and integrable discrete and continuous systems

Cited by in corpus (1)

• Discrete exponential type systems on a quad graph, corresponding to the affine Lie algebras $A_{N-1}^{(1)}$