Laplace type invariants for parabolic equations
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.
Hyperbolic, elliptic and parabolic equations
scientific article; zbMATH DE number 1784462