Symmetry, compatibility and exact solutions of PDEs
Differential Geometry
2012-03-06 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1111.5856,
title = {Symmetry, compatibility and exact solutions of PDEs},
author = {Boris Kruglikov},
journal= {arXiv preprint arXiv:1111.5856},
year = {2012}
}
Comments
Two more examples are added to section 2