×

Non-classical symmetry reduction: Example of the Boussinesq equation. (English) Zbl 0694.35159

Summary: A symmetry of an equation will leave the set of all solutions invariant. A ‘conditional symmetry’ will leave only a subset of solutions, defined by some differential condition, invariant. We show how a specific class of conditional symmetries can be used to reduce a partial differential equation to an ordinary one. In particular, for the Boussinesq equation, these conditional symmetries, together with the ordinary ones, provide all possible reductions to ordinary differential equations. A group theoretical explanation of the recently obtained new reductions is provided.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35A22 Transform methods (e.g., integral transforms) applied to PDEs
PDFBibTeX XMLCite
Full Text: DOI