On a discrete Davey-Stewartson system
Gegenhasi, Xing-Biao Hu, Decio Levi
Abstract
We propose a differential difference equation in R1× Z2 and study it by Hirota's bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson equation. The solutions of this discrete DS system are characterized by Casorati and Grammian determinants. Based on the bilinear form of this discrete DS system, we construct the bilinear Bäcklund transformation which enables us to obtain its Lax pair.
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