GROUP-INVARIANT SOLUTIONS OF DIFFERENTIAL EQUATIONS.

Peter J. Olver, Philip Rosenau

Research output: Contribution to journalArticlepeer-review

188 Scopus citations

Abstract

We introduce the concept of a weak symmetry group of a system of partial differential equations, that generalizes the 'nonclassical' method introduced by G. W. Bluman and J. D. Cole for finding group-invariant solutions to partial differential equations. Given any system of partial differential equations, it is shown how, in principle, to construct group-invariant solutions for any group of transformations by reducing the number of variables in the system. Conversely, every solution of the system can be found using this reduction method with some weak symmetry group.

Original languageEnglish (US)
Pages (from-to)263-278
Number of pages16
JournalSIAM Journal on Applied Mathematics
Volume47
Issue number2
DOIs
StatePublished - 1987

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