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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 $$u_{tt}-u_{xx}+\bigl(f(u)+ u_{xx}\bigr)_{xx} =0,$$ 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:
 35Q53 KdV-like (Korteweg-de Vries) equations 37K30 Relations of infinite-dimensional systems with algebraic structures 35A30 Geometric theory for PDE, characteristics, transformations
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