论文标题
3D二次Zakharov-Kuznetsov方程的孤立波的渐近稳定性
Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation
论文作者
论文摘要
我们考虑二次Zakharov-kuznetsov方程$$ \ partial_t u + \partial_xΔU + \ partial_x u^2 = 0 $ \ on $ \ mathbb {r}^3 $。单独的波解决方案由$ q（x-t，y，z）$给出，其中$ q $是$ -Q +ΔQ + q^2 = 0 $的基态解决方案。我们证明了这些孤立波解的渐近稳定性。 Specifically, we show that initial data close to $Q$ in the energy space, evolves to a solution that, as $t\to\infty$, converges to a rescaling and shift of $Q(x-t,y,z)$ in $L^2$ in a rightward shifting region $x> δt -\tan θ\sqrt{y^2+z^2} $ for $0 \leq θ\leq \fracπ{3}-Δ$。
We consider the quadratic Zakharov-Kuznetsov equation $$ \partial_t u + \partial_x Δu + \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 $-Q + ΔQ + Q^2 =0$. We prove the asymptotic stability of these solitary wave solutions. Specifically, we show that initial data close to $Q$ in the energy space, evolves to a solution that, as $t\to\infty$, converges to a rescaling and shift of $Q(x-t,y,z)$ in $L^2$ in a rightward shifting region $x> δt -\tan θ\sqrt{y^2+z^2} $ for $0 \leq θ\leq \fracπ{3}-δ$.
