We propose a differential difference equation in R-1 x 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 (DS) 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 Backlund transformation which enables us to obtain its Lax pair.
Gegenhasi, ., Hu, X.b., Levi, D. (2006). On a discrete Davey-Stewartson system. INVERSE PROBLEMS, 22(5), 1677-1688 [10.1088/0266-5611/22/5/009].
On a discrete Davey-Stewartson system
LEVI, Decio
2006-01-01
Abstract
We propose a differential difference equation in R-1 x 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 (DS) 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 Backlund transformation which enables us to obtain its Lax pair.File in questo prodotto:
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