The discrete potential Boussinesq equation and its multisoliton solutions

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.

17 pages,To appear in Applicable Analysis, Special Issue of Continuous and Discrete Integrable Systems

References in corpus (4)

• On a family of solutions of the KP equation which also satisfy the Toda lattice hierarchy
• Soliton solutions of the Kadomtsev-Petviashvili II equation
• Young diagrams and N-soliton solutions of the KP equation
• Classification of the line-soliton solutions of KPII

Cited by in corpus (5)

• Boussinesq-like multi-component lattice equations and multi-dimensional consistency
• Bäcklund Transformations for the Boussinesq Equation and Merging Solitons
• Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
• Integrable delay-difference and delay-differential analogues of the KdV, Boussinesq, and KP equations
• Matrix Boussinesq solitons and their tropical limit