On integrable reductions of two-dimensional Toda-type lattices

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 nonlinear Schrödinger type. 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. To celebrate 120 years from the day of birth of A. Kolmogorov

Keywords

• Integrability in sense of Darboux
• Generating function of integrals
• Lax pairs
• Liouville type equations
• Volterra chain