On a (2+1)-dimensional generalization of the Ablowitz-Ladik lattice and a discrete Davey-Stewartson system

Abstract

We propose a natural (2+1)-dimensional generalization of the Ablowitz-Ladik lattice that is an integrable space discretization of the cubic nonlinear Schroedinger (NLS) system in 1+1 dimensions. By further requiring rotational symmetry of order 2 in the two-dimensional lattice, we identify an appropriate change of dependent variables, which translates the (2+1)-dimensional Ablowitz-Ladik lattice into a suitable space discretization of the Davey-Stewartson system. The space-discrete Davey-Stewartson system has a Lax pair and allows the complex conjugation reduction between two dependent variables as in the continuous case. Moreover, it is ideally symmetric with respect to space reflections. Using the Hirota bilinear method, we construct some exact solutions such as multidromion solutions.

arXiv comment30 pages; (v2) minor grammatical changes (v3) added references, to appear in J.Phys.A (v4) minor cosmetic changes

References in corpus (5)

• Integrable discretizations of derivative nonlinear Schroedinger equations
• Integrable discrete Schrodinger equations and a characterization of Prym varieties by a pair of quadrisecants
• Functional representation of the Ablowitz-Ladik hierarchy. II
• On a discrete Davey-Stewartson system
• A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

Cited by in corpus (2)

• Towards the classification of integrable differential-difference equations in 2 + 1 dimensions
• Integrable discretization of recursion operators and unified bilinear forms to soliton hierarchies