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Laplace type invariants for parabolic equations
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2002 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, 125-133 p.Article in journal (Refereed) Published
Abstract [en]

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.

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Keyword [en]
hyperbolic, elliptic and parabolic equations, equivalence transformation, seminvariants, Laplace type invariants
National Category
Mathematical Analysis Mathematics
URN: urn:nbn:se:bth-8161ISI: 000174933300003Local ID: diva2:835850
Available from: 2012-09-18 Created: 2009-05-08 Last updated: 2015-06-30Bibliographically approved

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