Necessary integrability conditions for evolutionary lattice equations
Abstract
The structure of solutions is studied for the Lax equation Dt(G)=[F,G] for formal power series with respect to the shift operator. It is proved that if the equation with a given series F of degree m admits a solution G of degree k then it admits, as well, a solution H of degree m such that Hk=Gm. This property is used for derivation of necessary integrability conditions for scalar evolutionary lattices.
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