## 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
Full Text: