On a two-parameter extension of the lattice KdV system associated with an elliptic curve

Abstract

A general structure is developed from which a system of integrable partial difference equations is derived generalising the lattice KdV equation. The construction is based on an infinite matrix scheme with as key ingredient a (formal) elliptic Cauchy kernel. The consistency and integrability of the lattice system is discussed as well as special solutions and associated continuum equations.

Submitted to the proceedings of the Oeresund PDE-symposium, 23-25 May 2002; 17 pages LaTeX, style-file included

References in corpus (3)

• Classification of integrable equations on quad-graphs. The consistency approach
• Lax pair for the Adler (lattice Krichever-Novikov) System
• Integrable systems on quad-graphs

Cited by in corpus (8)

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• Integrability and Symmetries of Difference Equations: the Adler-Bobenko-Suris Case
• Linear integral equations, infinite matrices, and soliton hierarchies
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• On an elliptic extension of the Kadomtsev-Petviashvili equation
• The Sylvester equation and the elliptic Korteweg-de Vries system
• Elliptic Solutions of ABS Lattice Equations
• The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation