B. Lars G. Jonsson
Explicit solitary-wave ground states in one dimension
(115K, Postscript)

ABSTRACT.  We give explicit solutions, that decay to zero at infinity, to the class of equations 
\begin{equation*} 
-\partial_x^2 Q + c Q - \beta Q^{2p+1}- \alpha Q^{p+1}=0, 
\end{equation*} 
where $c>0$, $\beta>0$, $p>0$ and $\alpha\in \mathbb{R}$. This class 
of equations appears as the equation for the ground state for a 
solitary wave in the generalized nonlinear Schr\"{o}dinger equation 
in one dimension and in the generalized KdV equation.