Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation
Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation
Abstract: We consider the quadratic Zakharov-Kuznetsov equation $$\partial_t u + \partial_x \Delta u + \partial_x u^2=0$$ on $\Bbb{R}^3$. 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 the asymptotic stability of these solitary wave solutions. Specifically, we show that …