On a discrete Davey-Stewartson system

Details On a discrete Davey-Stewartson system On a discrete Davey-Stewartson system

2006-04-26

arxiv.org/abs/nlin/0604066v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, 2 figures

Scientific paper

10.1088/0266-5611/22/5/009

We propose a differential difference equation in ${\mathcal R}^1\times {\mathcal Z}^2$ 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 B\"{a}cklund transformation which enables us to obtain its Lax pair.

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