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Invariants of hyperbolic equations: Solution of the Laplace problem.
Responsible organisation
2004 (English)In: Journal of Applied Mechanics and Technical Physics, ISSN 0021-8944 (Print) 1573-8620 (Online), Vol. 45, no 2, 158-166 p.Article in journal (Refereed) PublishedAlternative title
Invariants of hyperbolic equations : Solution of the Laplace problem. (Swedish)
Abstract [en]

The renown Laplace invariants were used by P.S. Laplace in 1773 in his integration theory of linear hyperbolic differential equations in two variables. In 1960, L.V.Ovsyannikov, tackling the problem of group classification of hyperbolic equations, came across two proper invariants that do not change under the most general equivalence transformation of hyperbolic equations. The question on existence of other invariants remained open. The present paper is dedicated to solution of Laplace's problem which consists in finding all invariants for hyperbolic equations and constructing a basis of invariants. Three new invariants of first and second order as well as operators of invariant differentiations are constructed. It is shown that the new invariants, together with Ovsyannikov's invariants, provide a basis of invariants, so that any invariant of higher order is a function of the basic invariants and their invariant derivatives.

Place, publisher, year, edition, pages
New York: Springer , 2004. Vol. 45, no 2, 158-166 p.
Keyword [en]
Invariants, hyperbolic equations, Laplace's problem, Ovsyannikov's invariants, Lie group analysis, symmetries
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:bth-8847Local ID: oai:bth.se:forskinfo6D5189A0A02DF1B4C12573BE006246B6OAI: oai:DiVA.org:bth-8847DiVA: diva2:836602
Available from: 2012-09-18 Created: 2007-12-27 Last updated: 2015-06-30Bibliographically approved

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