Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-03-25
J. Phys. A: Math. Theor. 44 (2011) 325206
Nonlinear Sciences
Exactly Solvable and Integrable Systems
30 pages; (v2) minor grammatical changes (v3) added references, to appear in J.Phys.A (v4) minor cosmetic changes
Scientific paper
10.1088/1751-8113/44/32/325206
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.
Dimakis Aristophanes
Tsuchida Takayuki
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