论文标题
关于关键Korteweg-de Vries和Gardner方程的周期性行驶波的光谱稳定性
On the spectral stability of periodic traveling waves for the critical Korteweg-de Vries and Gardner equations
论文作者
论文摘要
在本文中，我们确定了关键的Korteweg-De Vries和Gardner方程的周期性波的光谱稳定性结果。对于第一个方程式，我们表明，正和零平均周期性波动解决方案都具有阈值，这可能使我们在光谱稳定性中破裂。关于第二个方程，我们在修改后的korteweg-de vries方程和两个方程式上使用galilean转换建立了周期性波的存在，阈值是相同的。本文中提出的主要优势涉及解决一些辅助初始值问题以获得光谱稳定性。
In this paper, we determine spectral stability results of periodic waves for the critical Korteweg-de Vries and Gardner equations. For the first equation, we show that both positive and zero mean periodic traveling wave solutions possess a threshold value which may provides us a rupture in the spectral stability. Concerning the second equation, we establish the existence of periodic waves using a Galilean transformation on the periodic cnoidal solution for the modified Korteweg-de Vries equation and for both equations, the threshold values are the same. The main advantage presented in our paper concerns in solving some auxiliary initial value problems to obtain the spectral stability.
