Non-classical symmetry reduction: example of the Boussinesq equation

Publisher Website
Google Scholar
Abstract
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. The authors 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.