| Abstract: | This paper considers the $
\mathcal{P}\mathcal{T}
$
\mathcal{P}\mathcal{T}
-symmetric extensions of the equations examined by Cooper, Shepard and Sodano. From the scaling properties of the $
\mathcal{P}\mathcal{T}
$
\mathcal{P}\mathcal{T}
-symmetric equations a general theorem relating the energy, momentum and velocity of any solitarywave solution of the generalized
KdV equation is derived. We also discuss the stability of the compacton solution as a function of the parameters affecting
the nonlinearities. |
