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2D-Schrödinger operator, \((2+1)\) evolution systems and new reductions, 2D-Burgers hierarchy and inverse problem data. (English. Russian original) Zbl 1231.35199

Russ. Math. Surv. 65, No. 3, 580-582 (2010); translation from Uspekhi Mat. Nauk. 65, No. 3, 195-196 (2010).
The paper discusses integrable systems in dimension (2+1) associated with the Lax pair operators in the form \(L=\partial_x\partial_y +G\partial_y + S\) and \(H=\partial_x^2+\partial_y^2+F\partial_y +A\) (the so-called GKMMN systems) and the related problems such as real reductions, reductions to the 2D-Burgers hierarchies, structure of the manifold of the Bloch-Floquet eigenfunctions, and associated algebro-geometric inverse spectral problems.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35R30 Inverse problems for PDEs
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