Levi, D.; Winternitz, P. Non-classical symmetry reduction: Example of the Boussinesq equation. (English) Zbl 0694.35159 J. Phys. A, Math. Gen. 22, No. 15, 2915-2924 (1989). 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. Cited in 2 ReviewsCited in 119 Documents MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application 35A22 Transform methods (e.g., integral transforms) applied to PDEs Keywords:symmetry; Boussinesq equation; conditional symmetries; reductions to ordinary differential equations PDFBibTeX XMLCite \textit{D. Levi} and \textit{P. Winternitz}, J. Phys. A, Math. Gen. 22, No. 15, 2915--2924 (1989; Zbl 0694.35159) Full Text: DOI