Multisoliton solutions to the lattice Boussinesq equation

The lattice Boussinesq equation (BSQ) is a three-component difference-difference equation defined on an elementary square of the two-dimensional lattice, having three-dimensional consistency. We write the equations in the Hirota bilinear form and construct their multisoliton solutions in terms of Ca...

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Bibliographic Details
Published in:Journal of mathematical physics 2010-03, Vol.51 (3), p.033505-033505-12
Main Authors: Hietarinta, Jarmo, Zhang, Da-jun
Format: Article
Language:English
Subjects:
Differential equations
Exact sciences and technology
Lattice theory
Mathematical methods in physics
Mathematical models
Mathematics
Physics
Quantum physics
Sciences and techniques of general use
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Summary:The lattice Boussinesq equation (BSQ) is a three-component difference-difference equation defined on an elementary square of the two-dimensional lattice, having three-dimensional consistency. We write the equations in the Hirota bilinear form and construct their multisoliton solutions in terms of Casoratians, following the methodology in our previous papers. In the construction it turns out that instead of the usual discretization of the exponential as [ ( a + k ) / ( a − k ) ] n , we need two different terms [ ( a − ω k ) / ( a − k ) ] n and [ ( a − ω 2 k ) / ( a − k ) ] n , where ω is a cubic root of unity ≠ 1 .
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3280362