Orbital stability of a generalized KdV solitary wave
= Orbital stability of a generalized KdV solitary wave
{c}
For the integer powers $p=2,3,4$ and $c>0$, the positive decaying <Generalized KdV solitary wave> is orbitally stable in $H^1(\mathbb R)$ modulo spatial translations. The variational slope has the stable sign because
$$
\|Q_c\|_2^2
=c^{(5-p)/(2(p-1))}\|Q\|_2^2
$$
is strictly increasing in $c$. Conserved mass and energy then furnish a Lyapunov functional transverse to the translation orbit.