Soliton solutions for ABS lattice equations: II. Casoratians and bilinearization

2009/03/10 by Jarmo Hietarinta, Da-jun Zhang, Da‐jun Zhang · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Geometry and complex manifolds #Lattice (music) #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #nlin.SI

paper · pdf · doi:10.1088/1751-8113/42/40/404006

published as J. Phys. A: Math. Theor. 42 (2009) 404006 · 36 pages

arxiv created 2009/03/10 · openalex publication_date 2009/09/16 · arxiv updated 2011/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In Part I 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, the central role was played by a Cauchy matrix. In this work we use a different approach, and 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.

Cited by

• Discrete Gerdjikov-Ivanov models and their higher-order counterparts from the Cauchy matrix scheme
• On consistency around a 3 × 3× 3 cube and Q3 analogue of the lattice Boussinesq equation

Related

• Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
• Solutions to the non-autonomous ABS lattice equations: Casoratians and bilinearization
• Solutions to the ABS lattice equations via generalized Cauchy matrix approach
• Elliptic Solutions of ABS Lattice Equations
• Soliton solutions for Q3