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29 March 2024
 
  » arxiv » 0906.3955

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Multisoliton solutions to the lattice Boussinesq equation
Jarmo Hietarinta ; Da-jun Zhang ;
Date 22 Jun 2009
AbstractThe lattice Boussinesq equation (BSQ) is a three-component difference-difference equation defined on an elementary square of the 2D lattice, having 3D 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 $[(a-omega k)/(a-k)]^n$ and $[(a-omega^2 k)/(a-k)]^n$, where $omega$ is a cubic root of unity $ eq 1$.
Source arXiv, 0906.3955
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