Formal diagonalization of a discrete lax operator and conservation laws and symmetries of dynamical systems
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We consider the problem of constructing a formal asymptotic expansion in the spectral parameter for an eigenfunction of a discrete linear operator. We propose a method for constructing an expansion that allows obtaining conservation laws of discrete dynamical systems associated with a given linear operator. As illustrative examples, we consider known nonlinear models such as the discrete potential Kortewegde Vries equation, the discrete version of the derivative nonlinear Schrödinger equation, the Veselov-Shabat dressing chain, and others. We describe the infinite set of conservation laws for the discrete Toda chain corresponding to the Lie algebra A 1 (1) . We find new examples of integrable systems of equations on a square lattice.
KeywordsLax pair asymptotic expansion conservation law symmetry equations on a quad graph discrete nonlinear Schrödinger equation dressing method
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