Discrete Dubrovin Equations and Separation of Variables for Discrete Systems

Abstract

A universal system of difference equations associated with a hyperelliptic curve is derived constituting the discrete analogue of the Dubrovin equations arising in the theory of finite-gap integration. The parametrisation of the solutions in terms of Abelian functions of Kleinian type (i.e. the higher-genus analogues of the Weierstrass elliptic functions) is discussed as well as the connections with the method of separation of variables.

Talk presented at the Intl. Conf. on ``Integrability and Chaos in Discrete Systems'', July 2-6, 1997, to appear in: Chaos, Solitons and Fractals, ed. F. Lambert, (Pergamon Press)

References in corpus (2)

• Few remarks on Baecklund transformations for many-body systems
• Separation of variables for the Ruijsenaars system

Cited by in corpus (8)

• Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions
• Hyperelliptic Solutions of Modified Korteweg-de Vries Equation of Genus g: Essentials of Miura Transformation
• Bäcklund Transformations as exact integrable time-discretizations for the trigonometric Gaudin model
• Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps
• Closed-form modified Hamiltonians for integrable numerical integration schemes
• Quantum discrete Dubrovin equations
• Integrable symplectic maps associated with discrete Korteweg-de Vries-type equations
• Soliton Solutions of Kortweg-de Vries Equations and Hyperelliptic Sigma Functions