Multisoliton solutions to the lattice Boussinesq equation

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 $[(a-\omega k)/(a-k){]}^n$ and $[(a-{\omega }^{2}k)/(a-k){]}^n$, where $\omega$ is a cubic root of unity $\ne 1$.

12 pages

References in corpus (2)

• Notes on solutions in Wronskian form to soliton equations: KdV-type
• The Boussinesq integrable system. Compatible lattice and continuum structures

Cited by in corpus (17)

• Soliton Taxonomy for a Modification of the Lattice Boussinesq Equation
• Bäcklund Transformations for the Boussinesq Equation and Merging Solitons
• Multi-Component Extension of CAC Systems
• Rational Solutions of the H3 and Q1 Models in the ABS Lattice List
• A higher-rank version of the Q3 equation
• Conservation laws of some lattice equations
• Discrete Boussinesq-type equations
• Integrability of auto-Bäcklund transformations,and solutions of a torqued ABS equation
• Solutions to the ABS lattice equations via generalized Cauchy matrix approach
• Direct Linearization of extended lattice BSQ systems
• From auto-Bäcklund transformations to auto-Bäcklund transformations, and torqued ABS equations
• Rational solutions to the ABS list: Degenerating approach
• On the Fourth-Order Lattice Gel'fand-Dikii Equations
• Spectrum transformation and conservation laws of the lattice potential KdV equation
• Binary Darboux transformations for discrete modified Boussinesq equation
• Elliptic solutions of Boussinesq type lattice equations and the elliptic Nth root of unity
• Convergence acceleration algorithm via an equation related to the lattice Boussinesq equation