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Invariant Lagrangians and a new method of integration of nonlinear equations.
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2005 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 304, no 1, 212-235 p.Article in journal (Refereed) Published
Abstract [en]

A method for solving the inverse variational problem for differential equations admitting a Lie group is presented. The method is used for determining invariant Lagrangians and integration of second-order nonlinear differential equations admitting two-dimensional non-commutative Lie algebras. The method of integration suggested here is different from Lie's classical method of integration of second-order ordinary differential equations based on canonical forms of two-dimensional Lie algebras. The new method reveals existence and significance of one-parameter families of singular solutions to nonlinear equations of second order.

Place, publisher, year, edition, pages
The Netherlands: ACADEMIC PRESS INC ELSEVIER SCIENCE , 2005. Vol. 304, no 1, 212-235 p.
Keyword [en]
Invariant, Lagrangians, nonlinear equations, Lie algebras, inverse variational problem.
National Category
Mathematical Analysis
URN: urn:nbn:se:bth-8841DOI: 10.1016/j.jmaa.2004.09.018ISI: 000227733900016Local ID: diva2:836596
Available from: 2012-09-18 Created: 2007-12-27 Last updated: 2015-06-30Bibliographically approved

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