Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds. (English. Russian original) Zbl 0928.35107

Novikov, S. P.; Dynnikov, I. A.

Russ. Math. Surv. 52, No. 5, 1057-1116 (1997); translation from Usp. Mat. Nauk 52, No. 5, 175-234 (1997).

The paper bears a resemblance to a review paper presenting a concise exposition of the algebraic picture of the Bäcklund-Darboux chains from the viewpoint of the rigorous spectral theory. While the rigorous completeness of the picture has not been proved in general, “\(\dots\) the problem may be considered more or less solved”. Numerous examples illustrate various aspects of the themes covered.

Reviewer: Nikolai L.Vulchanov (Warszawa)

MSC:

35P05	General topics in linear spectral theory for PDEs
39A70	Difference operators
47B39	Linear difference operators

Keywords:

Laplace-transformations; factorization; Bäcklund-Darboux chains