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arXiv · 1111.5856

Symmetry, compatibility and exact solutions of PDEs

Boris Kruglikov
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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 with respect to this Lie algebra. These conditions hold for generic=nondegenerate pairs (equation,symmetry) in certain dimension range for the Lie algebra. Finally we discuss models of equations with large symmetry algebras, which eventually lead to integration in closed form.

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Boris Kruglikov. 2011-11-24. Symmetry, compatibility and exact solutions of PDEs. https://arxiv.org/abs/1111.5856

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