Laplace type invariants for parabolic equations
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences2002 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, 125-133 p.Article in journal (Refereed) Published
The Laplace invariants pertain to linear hyperbolic differential equations with two independent variables. They were discovered by Laplace in 1773 and used in his integration theory of hyperbolic equations. Cotton extended the Laplace invariants to elliptic equations in 1900. Cotton's invariants can be obtained from the Laplace invariants merely by the complex change of variables relating the elliptic and hyperbolic equations. To the best of my knowledge, the invariants for parabolic equations were not found thus far. The purpose of this paper is to fill this gap by considering what will be called Laplace type invariants (or seminvariants), i.e. the quantities that remain unaltered under the linear transformation of the dependent variable. Laplace type invariants are calculated here for all hyperbolic, elliptic and parabolic equations using the unified infinitesimal method. A new invariant is found for parabolic equations.
Place, publisher, year, edition, pages
DORDRECHT: KLUWER ACADEMIC PUBL , 2002. 125-133 p.
hyperbolic, elliptic and parabolic equations, equivalence transformation, seminvariants, Laplace type invariants
Mathematical Analysis Mathematics
IdentifiersURN: urn:nbn:se:bth-8161ISI: 000174933300003Local ID: oai:bth.se:forskinfo7E947603A8B7EB39C12575B00021057EOAI: oai:DiVA.org:bth-8161DiVA: diva2:835850