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- Title
Symmetry, Compatibility and Exact Solutions of PDEs.
- Authors
Kruglikov, Boris
- Abstract
We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a Lie algebra of symmetries has invariant solutions. Finally we discuss models of equations with large symmetry algebras, which eventually lead to integration in closed form.
- Subjects
MATHEMATICAL symmetry; PARTIAL differential equations; DIFFERENTIAL operators; INVARIANTS (Mathematics); DARBOUX transformations; LIE algebras; MATHEMATICAL models
- Publication
Acta Applicandae Mathematicae, 2012, Vol 120, Issue 1, p219
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-012-9708-0