Soliton Solutions for ABS Lattice Equations II: Casoratians and Bilinearization

Abstract

In Part I [arXiv:0902.4873 [nlin.SI]] soliton solutions to the ABS list of multi-dimensionally consistent difference equations (except Q4) were derived using connection between the Q3 equation and the NQC equations, and then by reductions. In that work central role was played by a Cauchy matrix. In this work we use a different approach, we derive the $N$-soliton solutions following Hirota's direct and constructive method. This leads to Casoratians and bilinear difference equations. We give here details for the H-series of equations and for Q1; the results for Q3 have been given earlier.

36 pages

References in corpus (3)

• Soliton solutions for Q3
• Backlund transformations for integrable lattice equations
• Bilinearization and Casorati determinant solution to the non-autonomous discrete KdV equation

Cited by in corpus (24)

• Multisoliton solutions to the lattice Boussinesq equation
• On non-multiaffine consistent-around-the-cube lattice equations
• Elliptic soliton solutions: $\tau$ functions, vertex operators and bilinear identities
• Darboux and binary Darboux transformations for discrete integrable systems 1. Discrete potential KdV equation
• Weak Lax pairs for lattice equations
• Multi-Component Extension of CAC Systems
• Rational Solutions to the ABS List: Transformation Approach
• A multidimensionally consistent version of Hirota's discrete KdV equation
• Rational Solutions of the H3 and Q1 Models in the ABS Lattice List
• A variational perspective on continuum limits of ABS and lattice GD equations
• Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation
• Algebro-geometric solutions to the lattice potential modified Kadomtsev--Petviashvili equation
• Conservation laws of some lattice equations
• Integrability of auto-Bäcklund transformations,and solutions of a torqued ABS equation
• Discrete Crum's Theorems and Integrable Lattice Equations
• Discrete Boussinesq-type equations
• Explicit solutions for a nonlinear model on the honeycomb and triangular lattices
• A Revisit to the ABS H2 Equation
• Algebraic entropy for hex systems
• Elliptic Solutions of ABS Lattice Equations
• Spectrum transformation and conservation laws of the lattice potential KdV equation
• On the Fourth-Order Lattice Gel'fand-Dikii Equations
• Solutions to the non-autonomous ABS lattice equations: Casoratians and bilinearization
• Classification of integrable boundary equations for integrable quad-graph systems