论文标题
3D Zakharov-Kuznetsov方程中的孤子稳定性，分辨率和相互作用的数值研究
Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation
论文作者
论文摘要
我们在三个空间维度上介绍了Zakharov-Kuznetsov方程解决方案的详细数值研究。该方程是Korteweg-de Vries方程的三维概括，不完全可以集成。该方程为$ l^2 $ - 缩写，因此，解决方案在全球存在，例如，在$ h^1 $的能量空间中。 我们首先研究具有各种大小和对称性的各种扰动的孤子的稳定性，并显示出渐近稳定性和辐射的形成，证实了较大的初始数据的渐近稳定性导致\ cite {fhry2020}。然后，我们研究了不同的局部定位和衰减速率的溶液行为，包括指数和代数衰减，并对该方程中的孤子分辨率猜想给出积极的确认。最后，我们研究了各种环境中的孤子相互作用，并表明当两个孤子合并为一个时，既有准弹性相互作用又有很强的相互作用，在所有情况下，在所有情况下总是在负$ x $ the的圆锥形区域中发射辐射。
We present a detailed numerical study of solutions to the Zakharov-Kuznetsov equation in three spatial dimensions. The equation is a three-dimensional generalization of the Korteweg-de Vries equation, though, not completely integrable. This equation is $L^2$-subcritical, and thus, solutions exist globally, for example, in the $H^1$ energy space. We first study stability of solitons with various perturbations in sizes and symmetry, and show asymptotic stability and formation of radiation, confirming the asymptotic stability result in \cite{FHRY2020} for a larger class of initial data. We then investigate the solution behavior for different localizations and rates of decay including exponential and algebraic decays, and give positive confirmation toward the soliton resolution conjecture in this equation. Finally, we investigate soliton interactions in various settings and show that there is both a quasi-elastic interaction and a strong interaction when two solitons merge into one, in all cases always emitting radiation in the conic-type region of the negative $x$-direction.
