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Zbl 0944.35084
Gandarias, M.L.; Bruzon, M.S.
Classical and nonclassical symmetries of a generalized Boussinesq equation. (English)
[J] J. Nonlinear Math. Phys. 5, No.1, 8-12 (1998). ISSN 1402-9251; ISSN 1776-0852/e

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 2000:: *35Q53 KdV-like equations
37K30 Relations with algebraic structures
35A30 Geometric theory for PDE, transformations

Keywords: symmetry reductions; Lie-group formalism; generalized Boussinesq equation; new exact solutions

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