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| We apply the Lie-group formalism to deduce symmetries of the
generalized Benjamin equation,
\begin{equation}\label{edp}u_{tt}+a(u^pu_x)_x+\beta u_{xxxx}=0\end{equation} where
$a$, $\beta$ and $p$ are arbitrary constants different to zero.
This kind of equation is one of the most important nonlinear partial differential equations,
used in the analysis of long wave in shallow water.
We make an analysis of the symmetry reductions of equation (\ref{edp}). In order to obtain travelling wave solutions we apply an indirect F-function method. We obtain some periodic wave solutions expressed by various single and combined nondegenerative Jacobi elliptic function solutions and their degenerative solutions. |
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