Symmetries of the heat equation on the lattice
type: Item
instance of: scholarly article
title: Symmetries of the heat equation on the lattice
zbMATH Open document ID: 0851.39007
DOI: 10.1007/BF00714402
author: R. Floreanini
author: J. Negro
author: Luc Vinet
author: Luis-Miguel Nieto
published in: Letters in Mathematical Physics
publication date: 1996-06-23T00:00:00Z
review text: The symmetry operators of the discrete version (1) \([\Delta_t- \Delta^2_x ]\varphi (t, x)= 0\), \((t, x)\in \mathbb{R}^2\) of the heat equation (HE) in one space dimension are presented. Here \(\Delta_a= {1\over C_a} [T_a- 1]\), \(T_a\) are the shift operators and \(C_a\) are the lattice constants. It turns out that this partial difference equation has the same symmetry algebra as its continuous limit -- the usual HE. Finally, this symmetry algebra is exploited to find some solutions of (1) and, next, to study their properties. Note also a similar study of the \(q\)-difference analog of the HE carried out by \textit{R. Floreanini} and \textit{L. Vinet} [Lett. Math. Phys. 32, No. 1, 37-44 (1994; Zbl 0805.39008)].
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 81T25
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 878268
zbMATH Keywords: heat equation
zbMATH Keywords: partial difference equation
zbMATH Keywords: symmetry algebra
reviewed by: Elena Trofimchuk
MaRDI profile type: Publication
cites work: Symmetries of the \(q\)-difference heat equation
cites work: Quantum symmetries of q-difference equations
cites work: Lie theory and difference equations. I
cites work: Quantum mechanics and polynomials of a discrete variable
description: scientific article; zbMATH DE number 878268