On integrable reductions of two-dimensional Toda-type lattices
arXiv:2405.10666
Abstract
The article considers lattices of the two-dimensional Toda type, which can be interpreted as dressing chains for spatially two-dimensional generalizations of equations of the class of nonlinear Schrödinger equations. The well-known example of this kind of generalization is the Davey-Stewartson equation. It turns out that the finite-field reductions of these lattices, obtained by imposing cutoff boundary conditions of an appropriate type, are Darboux integrable, i.e., they have complete sets of characteristic integrals. An algorithm for constructing complete sets of characteristic integrals of finite field systems using Lax pairs and Miura-type transformations is discussed.
20 pages