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Non-classical symmetry reduction: example of the Boussinesq equation

1989; Institute of Physics; Volume: 22; Issue: 15 Linguagem: Inglês

10.1088/0305-4470/22/15/010

1361-6447

D. Levi, P. Winternitz,

Nonlinear Photonic Systems

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.