Abstract
A differential-difference Davey-Stewartson system with self-consistent sources is constructed using the source generation procedure. We observe how the resulting coupled discrete system reduces to the identities for determinant by presenting the Gram-type determinant solution and Casorati-type determinant solution.
Highlights
The study of discrete integrable system has become an active area of research for over thirty years
In [7], the authors applied the modified Hirota’s approach to the Davey-Stewartson system to produce an integrable differential-difference Davey-Stewartson system which is characterized by determinant solutions, bilinear Bäcklund transformation and lax pair. This differential-difference Davey-Stewartson system can be derived as a reduction of a (2 +1) -dimensional generalization of the Ablowitz-Ladik lattice [8]
In [7], a differential-difference Davey-Stewartson system which is an integrable discretization of the DSI system is proposed, and the double-Casorati and Grammian determinants solutions to this discrete Davey-Stewartson system are derived
Summary
The study of discrete integrable system has become an active area of research for over thirty years. We apply the source generalization procedure to construct and solve the differential-difference Davey-Stewartson system with self-consistent sources. 2. Constructing the Differential-Difference Davey-Stewartson System with Self-Consistent Sources
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