In this work, we consider the following generalized Boussinesq equation
\begin{align*}
\partial_{t}^2u-\partial_{x}^2u+\partial_{x}^2(\partial_{x}^2u+|u|^{p}u)=0,\qquad
(t,x)\in\mathbb R\times \mathbb R, \end{align*} with 0<p<β. This
equation has the traveling wave solutions ΟΟβ(xβΟt), with the
frequency Οβ(β1,1) and ΟΟβ satisfying \begin{align*}
-\partial_{xx}{\phi}_{\omega}+(1-{\omega^2}){\phi}_{\omega}-{\phi}_{\omega}^{p+1}=0.
\end{align*} Bona and Sachs (1988) proved that the traveling wave
ΟΟβ(xβΟt) is orbitally stable when 0<p<4,4pβ<Ο2<1. Liu (1993) proved the orbital instability under the conditions
0<p<4,Ο2<4pβ or pβ₯4,Ο2<1. In this paper, we prove
the orbital instability in the degenerate case 0<p<4,Ο2=4pβ .Comment: 29 page