论文标题
Zakharov-Kuznetsov方程的线孤子的横向稳定性的数值研究
Numerical study of the transverse stability of line solitons of the Zakharov-Kuznetsov equations
论文作者
论文摘要
我们介绍了一项详细的数值研究，对具有各种功率非线性的二维，广义Zakharov-Kuznetsov方程的线孔的周期性扰动。在$ l^{2} $ - 亚临界情况下，根据Yamazaki的定理，我们发现了一个临界速度，在该线路下方索尼顿线稳定下。对于较高的速度，数值结果表明对肿块形成的不稳定性，该肿块位于两个空间方向上。在$ l^2 $ - 关键和超批评的情况下，但对于1D广义的korteweg-de Vries方程式），显示圆线在小速度上是数值稳定的，对于大速度，对于大速度而言非常不稳定，在有限的时间内观察到爆炸。
We present a detailed numerical study of the stability under periodic perturbations of line solitons of two-dimensional, generalized Zakharov-Kuznetsov equations with various power nonlinearities. In the $L^{2}$-subcritical case, in accordance with a theorem due to Yamazaki we find a critical speed, below which the line soliton is stable. For higher velocities, the numerical results indicate an instability against the formation of lumps, solitons localized in both spatial directions. In the $L^2$-critical and supercritical cases but subcritical for the 1D generalized Korteweg-de Vries equation), the line solitons are shown to be numerically stable for small velocities, and strongly unstable for large velocities, with a blow-up observed in finite time.
