Rational Solutions to the ABS List: Transformation Approach

Abstract

In the paper we derive rational solutions for the lattice potential modified Korteweg-de Vries equation, and Q2, Q1($\delta$), H3($\delta$), H2 and H1 in the Adler-Bobenko-Suris list. Bäcklund transformations between these lattice equations are used. All these rational solutions are related to a unified $\tau$ function in Casoratian form which obeys a bilinear superposition formula.

References in corpus (9)

• Lax pair for the Adler (lattice Krichever-Novikov) System
• Soliton Solutions for ABS Lattice Equations: I Cauchy Matrix Approach
• Soliton Solutions for ABS Lattice Equations II: Casoratians and Bilinearization
• Boussinesq-like multi-component lattice equations and multi-dimensional consistency
• Soliton solutions for Q3
• Backlund transformations for integrable lattice equations
• Bilinearization of Discrete Soliton Equations and Singularity Confinement
• A constructive approach to the soliton solutions of integrable quadrilateral lattice equations
• Rational Solutions of the H3 and Q1 Models in the ABS Lattice List

Cited by in corpus (9)

• Multi-Component Extension of CAC Systems
• The solutions of classical and nonlocal nonlinear Schrödinger equations with nonzero backgrounds: Bilinearisation and reduction approach
• A variational perspective on continuum limits of ABS and lattice GD equations
• On decomposition of the ABS lattice equations and related Bäcklund transformations
• A Revisit to the ABS H2 Equation
• Rational solutions to the ABS list: Degenerating approach
• Symmetric discrete AKP and BKP equations
• Eigenfunction equations of lattice KdV equations and connections to ABS lattice equations with a $\delta$ term
• Addition formulae, Bäcklund transformations, periodic solutions and quadrilateral equations