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To a transformation theory of two-dimensional integrable systems. (English) Zbl 0962.37509

Summary: We generalise to the two-dimensional case a list of integrable Toda type lattice equations. As a result, \(1+2\) dimensional systems similar to the Davey-Stewartson coupled system are obtained together with explicit auto-Bäcklund transformations and 2D Miura type transformations.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q58 Other completely integrable PDE (MSC2000)
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