- 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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