Classical and nonclassical symmetries of a generalized Boussinesq equation

TL;DR

This paper uses Lie-group and nonclassical methods to analyze symmetries of a generalized Boussinesq equation, identifying conditions for symmetries and deriving new exact solutions.

Contribution

It extends symmetry analysis to a generalized Boussinesq equation, including classical and nonclassical symmetries, and derives new exact solutions.

Findings

Identified symmetry conditions for the generalized Boussinesq equation.

Derived reductions and new exact solutions.

Analyzed the special case of the classical Boussinesq equation.

Abstract

We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Boussinesq equation, which has the classical Boussinesq equation as an special case. We study the class of functions $f(u)$ for which this equation admit either the classical or the nonclassical method. The reductions obtained are derived. Some new exact solutions can be derived.