Soliton Taxonomy for a Modification of the Lattice Boussinesq Equation

TL;DR

This paper explores a modified lattice Boussinesq equation, analyzing soliton solutions influenced by a deformation parameter, and classifies these solutions within a new soliton taxonomy.

Contribution

It introduces a soliton taxonomy for a modified lattice Boussinesq equation with a nonzero deformation parameter, expanding understanding of soliton behavior in integrable lattice models.

Findings

Identification of soliton types depending on the deformation parameter

Analysis of soliton solutions within specific parameter ranges

Extension of integrable lattice equation classifications

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 $b_0>0$, which allows special kinds of solitons in the parameter range $-b_0/3<k<b_0$.