Multisoliton solutions to the lattice Boussinesq equation

2009/06/22 by Jarmo Hietarinta, Da-jun Zhang · 2 citations
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1063/1.3280362

published as J. Math. Phys. 51, 033505 (2010) · 12 pages

arxiv created 2009/06/22 · arxiv updated 2011/05/27

Abstract

The 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-ωk)/(a-k)]ⁿ and [(a-ω² k)/(a-k)]ⁿ, where ω is a cubic root of unity ≠ 1.

Cited by

• PGL(3)-invariant integrable systems from factorisation of linear differential and difference operators
• On consistency around a 3 × 3× 3 cube and Q3 analogue of the lattice Boussinesq equation