Invariant Lagrangians and a new method of integration of nonlinear equations.
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences2005 (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
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.
Invariant, Lagrangians, nonlinear equations, Lie algebras, inverse variational problem.
IdentifiersURN: urn:nbn:se:bth-8841DOI: 10.1016/j.jmaa.2004.09.018ISI: 000227733900016Local ID: oai:bth.se:forskinfoA43537C14D15709DC12573BE006ABD09OAI: oai:DiVA.org:bth-8841DiVA: diva2:836596