| Abstract: |
| We consider the quadratic Zakharov-Kuznetsov equation
$$\partial_t u + \partial_x \Delta u + \partial_x u^2 =0$$
on $\mathbb{R}^3$. A solitary wave solution is given by $Q(x-t,y,z)$, where $Q$ is the ground state solution to $-Q + \Delta Q + Q^2 =0$. We prove that solutions in the energy space that are orbitally stable, that is, remain close to the two-parameter manifold spanned by dilations and translations of $Q$, are in fact \emph{asymptotically} stable. Specifically, as $t\to\infty$, they converge to a rescaling and shift of $Q(x-t,y,z)$ in a rightward shifting window. |
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