论文标题
Zakharov-Kuznetsov方程的数值研究二维
Numerical study of Zakharov-Kuznetsov equations in two dimensions
论文作者
论文摘要
我们对（广义）Zakharov-Kuznetsov方程的解决方案进行了详细的数值研究，其中两个空间维度具有各种功率非线性。在$ l^{2} $ - 亚临界情况下，为孤子的稳定性和孤子分辨率提供了数值证据，以进行通用初始数据。在$ l^2 $ - 关键和超批评案件中，孤子似乎不稳定，不稳定分散和爆炸。猜想爆炸发生在有限的时间内，并且爆炸解决方案具有相似的相似之处，即爆炸核心形成向右移动的自相似类型的重新恢复的轮廓，而在关键情况下，爆炸发生在无限的情况下，并且在超批评的情况下是有限的位置。在$ l^{2} $ - 关键案例中，爆炸似乎与$ l^{2} $中的爆炸相似 - 关键的广义korteweg-de vries方程，该配置文件是动态重新定性的soliton。
We present a detailed numerical study of solutions to the (generalized) Zakharov-Kuznetsov equation in two spatial dimensions with various power nonlinearities. In the $L^{2}$-subcritical case, numerical evidence is presented for the stability of solitons and the soliton resolution for generic initial data. In the $L^2$-critical and supercritical cases, solitons appear to be unstable against both dispersion and blow-up. It is conjectured that blow-up happens in finite time and that blow-up solutions have some resemblance of being self-similar, i.e., the blow-up core forms a rightward moving self-similar type rescaled profile with the blow-up happening at infinity in the critical case and at a finite location in the supercritical case. In the $L^{2}$-critical case, the blow-up appears to be similar to the one in the $L^{2}$-critical generalized Korteweg-de Vries equation with the profile being a dynamically rescaled soliton.
