Symmetries of Discrete Systems

Abstract

In this series of lectures presented at the CIMPA Winter School on Discrete Integrable Systems in Pondicherry, India, in February, 2003 we give a review of the application of Lie point symmetries, and their generalizations to the study of difference equations. The overall theme of these lectures could be called "continuous symmetries of discrete equations".

58 pages, 5 figures, Lectures presented at the Winter School on Discrete Integrable Systems in Pondicherry, India, February 2003

References in corpus (3)

• Lie point symmetries of difference equations and lattices
• Continuous symmetries of Lagrangians and exact solutions of discrete equations
• Lie symmetries of multidimensional difference equations

Cited by in corpus (23)

• Integrable discretizations of the short pulse equation
• An integrable semi-discretization of the Camassa-Holm equation and its determinant solution
• Discrete Integrable Systems and Hodograph Transformations Arising from Motions of Discrete Plane Curves
• Desargues maps and the Hirota-Miwa equation
• The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
• A minimal-variable symplectic integrator on spheres
• Multidimensional Toda Lattices: Continuous and Discrete Time
• Symmetries of the Continuous and Discrete Krichever-Novikov Equation
• Infinitely many conservation laws for the discrete KdV equation
• Integrable Systems and Discrete Geometry
• Lie group analysis of a generalized Krichever-Novikov differential-difference equation
• Darboux transformations for linear operators on two dimensional regular lattices
• Machine-assisted discovery of integrable symplectic mappings
• Non-commutative q-Painleve VI equation
• Asymptotic symmetries of difference equations on a lattice
• Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation
• Umbral Vade Mecum
• ${\mathbb{Z}}_{\mathcal{N}}$ graded discrete integrable systems and Darboux transformations
• Discrete integrable systems, Darboux transformations, and Yang-Baxter maps
• Singularity confinement and proliferation of tau functions for a general differential-difference Sawada-Kotera equation
• Combinatorial Reduction of Set Functions and Matroid Permutations through Minor Product Assignment
• Integrable discretizations of a two-dimensional Hamiltonian system with a quartic potential
• Differential equations for the closed geometric crystal chains