Symmetry, compatibility and exact solutions of PDEs

Details Symmetry, compatibility and exact solutions of PDEs Symmetry, compatibility and exact solutions of PDEs

2011-11-24

arxiv.org/abs/1111.5856v2

Mathematics

Differential Geometry

Two more examples are added to section 2

Scientific paper

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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