Laplace type invariants for parabolic equations
type: Item
instance of: scholarly article
title: Laplace type invariants for parabolic equations
zbMATH Open document ID: 1065.35010
DOI: 10.1023/A:1015008716928
published in: Nonlinear Dynamics
publication date: 2002-08-20T00:00:00Z
review text: The Laplace invariants were discovered in the article [\textit{P. S. Laplace}, Recherches sur le calcul intégral aux différences partielles, Mém.Acad. R. Sci. Paris 1773/77, 341--402; reprinted in Laplace's Œuvres complètes, Vol. IX, Gauthier-Villars, Paris (1893), 5-68; Engl. transl. New York (1966)] and used in his integration theory of hyperbolic equations. In the article under review Laplace type invariants (i.e. the quantities that remain unaltered under the linear transformation of the dependent variables) are derived for all hyperbolic, elliptic and parabolic equations by means of a systematic infinitesimal method for calculating invariants of differential equations. A new invariant is found for parabolic equations.
Mathematics Subject Classification ID: 35A22
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35K10
zbMATH DE Number: 1784462
zbMATH Keywords: Hyperbolic, elliptic and parabolic equations
zbMATH Keywords: equivalence transformation
zbMATH Keywords: semiinvariants
zbMATH Keywords: Laplace type invariants
author: Nail H. Ibragimov
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1784462