Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 061, 14 pages      arXiv:1105.4413      https://doi.org/10.3842/SIGMA.2011.061
Contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)”

Soliton Taxonomy for a Modification of the Lattice Boussinesq Equation

Jarmo Hietarinta a, b and Da-jun Zhang c
a) Department of Physics and Astronomy, University of Turku, FIN-20014 Turku, Finland
b) LPTHE / CNRS / UPMC, 4 place Jussieu 75252 Paris CEDEX 05, France
c) Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China

Received May 24, 2011, in final form July 01, 2011; Published online July 06, 2011; Figure 3 changed July 20, 2011

Abstract
Integrable multi-component lattice equations of the Boussinesq family have been known for some time. Recently some new equations of this type were found using the Consistency-Around-the-Cube approach. Here we investigate one of these models, B-2, and in particular the consequences of a nonzero deformation parameter b0>0, which allows special kinds of solitons in the parameter range −b0/3<k<b0.

Key words: lattice Boussinesq equation; integrable lattice equations; solitons; kinks.

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