论文标题
Konopelchenko-Dubrovsky方程中的横向光谱不稳定性
Transverse Spectral Instabilities in Konopelchenko-Dubrovsky Equation
论文作者
论文摘要
我们研究了（2+1） - 维konopelchenko-dubrovsky（KD）方程的一维小振幅周期性波动溶液的横向光谱稳定性。我们表明，相对于二维扰动，这些波是横向不稳定的，这些扰动是在两个方向上周期性周期性的，在横向方向上有长波长。我们还表明，相对于扰动，这些波是横向稳定的，这些扰动是均值为零的周期性或方向，在波浪的传播方向上，并在横向沿有限或短波长的横向方向上进行周期性。我们讨论了这些结果对KD方程的特殊情况的含义 - 即KP-II和MKP-II方程。
We study the transverse spectral stability of the one-dimensional small-amplitude periodic traveling wave solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky (KD) equation. We show that these waves are transversely unstable with respect to two-dimensional perturbations that are periodic in both directions with long wavelength in the transverse direction. We also show that these waves are transversely stable with respect to perturbations which are either mean-zero periodic or square-integrable in the direction of the propagation of the wave and periodic in the transverse direction with finite or short wavelength. We discuss the implications of these results for special cases of the KD equation - namely, KP-II and mKP-II equations.
