04-153 B. Lars G. Jonsson
Explicit solitary-wave ground states in one dimension (115K, Postscript) May 14, 04
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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.

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