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Symmetry, Compatibility and Exact Solutions of PDEs

Symmetry, Compatibility and Exact Solutions of PDEs 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Symmetry, Compatibility and Exact Solutions of PDEs

Acta Applicandae Mathematicae , Volume 120 (1) – Mar 23, 2012

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References (42)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Science+Business Media B.V.
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Mathematics, general; Computer Science, general; Statistical Physics, Dynamical Systems and Complexity; Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-012-9708-0
Publisher site
See Article on Publisher Site

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.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Mar 23, 2012

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