Theoretical and Mathematical Physics

, Volume 181, Issue 2, pp 1367–1382 | Cite as

Necessary integrability conditions for evolutionary lattice equations

  • V. E. Adler


We study the structure of solutions of the Lax equation Dt(G) = [F,G] for formal series in powers of the shift operator. We show that if an equation with a given series F of degree m admits a solution G of degree k, then it also admits a solution H of degree m such that Hk = Gm. We use this property to derive necessary integrability conditions for scalar evolutionary lattices.


Volterra-type lattice higher symmetry conservation law integrability test 


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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRASChernogolovkaRussia

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