The discrete potential Boussinesq equation and its multisoliton solutions

TL;DR

This paper introduces an alternate discrete potential Boussinesq equation, constructs its multisoliton solutions, derives an ultradiscrete version, and explores its relation to existing lattice equations, advancing the understanding of integrable discrete systems.

Contribution

It proposes a new form of the discrete potential Boussinesq equation, constructs multisoliton solutions, and clarifies its relation to existing lattice equations using reduction and singularity confinement techniques.

Findings

Constructed multisoliton solutions for the new equation

Derived an ultradiscrete version via ultradiscretization

Clarified the relation to Nijhoff et al.'s lattice potential Boussinesq equation

Abstract

An alternate form of discrete potential Boussinesq equation is proposed and its multisoliton solutions are constructed. An ultradiscrete potential Boussinesq equation is also obtained from the discrete potential Boussinesq equation using the ultradiscretization technique. The detail of the multisoliton solutions is discussed by using the reduction technique. The lattice potential Boussinesq equation derived by Nijhoff et al. is also investigated by using the singularity confinement test. The relation between the proposed alternate discrete potential Boussinesq equation and the lattice potential Boussinesq equation by Nijhoff et al. is clarified.