Abstract
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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 2, pp. 252–263, February, 1998.
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Samoilenko, V.G., Sidorenko, Y.M. Hierarchy of the matrix Burgers equations and integrable reductions in the Davey-Stewartson system. Ukr Math J 50, 287–301 (1998). https://doi.org/10.1007/BF02513452
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DOI: https://doi.org/10.1007/BF02513452