Hierarchy of the matrix Burgers equations and integrable reductions in the Davey-Stewartson system
We investigate integrable reductions in the Davey-Stewartson model and introduce the hierarchy of the matrix Burgers equations. By using the method of nonlocal reductions in linear problems associated with the hierarchy of the Davey-Stewartson-II equations, we establish a nontrivial relation between these equations and a system of matrix Burgers equations. In an explicit form, we present reductions of the Davey-Stewartson-II model that admit linearization.
English version (Springer): Ukrainian Mathematical Journal 50 (1998), no. 2, pp 287-301.
Citation Example: Samoilenko V. G., Sidorenko Yu. M. Hierarchy of the matrix Burgers equations and integrable reductions in the Davey-Stewartson system // Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 252–263.