Formal diagonalization of the discrete Lax operators and construction of conserved densities and symmetries for dynamical systems

Abstract

An alternative method of constructing the formal diagonalization for the discrete Lax operators is proposed which can be used to calculate conservation laws and in some cases generalized symmetries for discrete dynamical systems. Discrete potential KdV equation, lattice derivative nonlinear Schrödinger equation, dressing chain, Toda lattice are considered as illustrative examples. For the Toda lattice on a quad graph corresponding to the Lie algebra $A_1^{(1)}$ infinite series of conservation laws are described. Systems of quad graph equations are represented including lattice versions of the "matrix" NLS and "vector" derivative NLS equations.

33 pages

References in corpus (3)

• Quantum and classical integrable sine-Gordon model with defect
• Recursion operators, conservation laws and integrability conditions for difference equations
• Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time

Cited by in corpus (7)

• On a method for constructing the Lax pairs for nonlinear integrable equations
• Formal diagonalisation of Lax-Darboux schemes
• Peculiar symmetry structure of some known discrete nonautonomous equations
• An unusual series of autonomous discrete integrable equations on the square lattice
• Asymptotic diagonalization of the Discrete Lax pair around singularities and conservation laws for dynamical systems
• Discrete exponential type systems on a quad graph, corresponding to the affine Lie algebras $A_{N-1}^{(1)}$
• Spectrum transformation and conservation laws of the lattice potential KdV equation