Lie symmetries of finite-difference equations

DOI10.1063/1.531205zbMath0859.39008OpenAlexW1971200802MaRDI QIDQ4873422

Luc Vinet, Roberto Floreanini

Publication date: 16 April 1996

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531205

zbMATH Keywords

Lie symmetrieslinear difference equationsdiscretized wave equationdiscretized heat equationdiscretized Helmholtz equationdiscretized Bessel functionsdiscretized Gegenbauer polynomialsdiscretized Hermite polynomialsdiscretized hypergeometric functionsdiscretized Laguerre polynomials

Mathematics Subject Classification ID

Heat equation (35K05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Wave equation (35L05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Additive difference equations (39A10) Discrete version of topics in analysis (39A12)

Related Items (20)

On Invariance Factors and Invariance Vectors for Difference Equations ⋮ Wavelets and quantum algebras ⋮ Lie group classification of first-order delay ordinary differential equations ⋮ Burchnall-Chaundy Theory for q-Difference Operators and q-Deformed Heisenberg Algebras ⋮ On symmetry-preserving difference scheme to a generalized Benjamin equation and third-order Burgers equation ⋮ Conservative invariant finite‐difference schemes for the modified shallow water equations in Lagrangian coordinates ⋮ Hojman conserved quantities of discrete mechanico-electrical systems constructed by continuous symmetries ⋮ UMBRAL DEFORMATIONS ON DISCRETE SPACE–TIME ⋮ Shallow water equations in Lagrangian coordinates: symmetries, conservation laws and its preservation in difference models ⋮ The symmetry-preserving difference schemes and exact solutions of some high-dimensional differential equations ⋮ Noether symmetries of discrete nonholonomic dynamical systems ⋮ On two-dimensional \(q\)-differential transform method ⋮ Lie group classification of second-order ordinary difference equations ⋮ Umbral calculus, difference equations and the discrete Schrödinger equation ⋮ Generalized conditional symmetries of nonlinear differential-difference equations ⋮ Discretization of nonlinear evolution equations over associative function algebras ⋮ Discrete shallow water equations preserving symmetries and conservation laws ⋮ Symmetries of discrete dynamical systems involving two species ⋮ Taylor polynomial stepwise refinement algorithm for Lie and high symmetries of partial differential equations ⋮ Invariant solutions for nonhomogeneous discrete diffusion equation

Cites Work

• Quantum mechanics and polynomials of a discrete variable
• Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
• Symmetries of the \(q\)-difference heat equation
• Lie theory and difference equations. I
• Canonical Equations and Symmetry Techniques forq-Series
• Quantum symmetries of q-difference equations
• Lie Theory and Generalizations of the Hypergeometric Functions

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