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Classical and nonclassical symmetries of a generalized Boussinesq equation. (English) Zbl 0944.35084

Summary: We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Boussinesq equation

u tt -u xx +f (u) + u xx xx =0,

which has the classical Boussinesq equation as an special case. We study the class of functions f(u) for which this equation admits either the classical or the nonclassical method. Symmetry reductions are obtained and some new exact solutions are derived.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
37K30Relations of infinite-dimensional systems with algebraic structures
35A30Geometric theory for PDE, characteristics, transformations