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| In this paper we make an analysis of the symmetry reductions
of the
nonlinear beam equation of Kirchoff type given by,
\begin{equation}\label{edp}
\Delta\equiv u_{tt}+u_{xxxx}-M\left(\int|u_x|^2dx\right)u_{xx}+\nu u_t=0.
\end{equation}
where $u=u(x,t)$ is the transverse deflection of beam which
changes its configuration at each instants of time, increasing its
deformation and hence increasing its tension.
We use the classical Lie method of
infinitesimals. We consider
travelling wave reductions depending on the form of an arbitrary
function. We present some reductions. |
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