论文标题
等温欧拉 - 波森系统的孤立波的线性稳定性
Linear Stability of solitary waves for the isothermal Euler-Poisson system
论文作者
论文摘要
我们研究了等温Euler-Poisson系统的两参数孤立波的渐近线性稳定性。当考虑有关孤立波的线性化方程式时，$ l^2 $空间中相关的特征值问题的特征值嵌入了中性频谱中，即没有光谱间隙。为了解决此问题，使用是由指数加权的$ l^2 $ norm制成的，因此本质频谱严格地转移到左半平面上，这与超级离子 - 苏联体制中存在的单个波浪密切相关。此外，在一定的长波长缩放中，我们表明埃文斯（Evans）的欧拉 - 波森系统（Evans）功能会收敛到korteweg-de vries（KDV）方程为振幅参数，趋向于零，我们从中我们从中介绍了原点是唯一具有其自然域具有其自然域而具有其algebraic multecraic poollical poollical tw的eigenvalue。我们还表明，孤独的波浪在$ l^2 $空间中是频谱稳定的。此外，我们讨论了大幅度孤立波的稳定性。
We study the asymptotic linear stability of a two-parameter family of solitary waves for the isothermal Euler-Poisson system. When the linearized equations about the solitary waves are considered, the associated eigenvalue problem in $L^2$ space has a zero eigenvalue embedded in the neutral spectrum, i.e., there is no spectral gap. To resolve this issue, use is made of an exponentially weighted $L^2$ norm so that the essential spectrum is strictly shifted into the left-half plane, and this is closely related to the fact that solitary waves exist in the super-ion-sonic regime. Furthermore, in a certain long-wavelength scaling, we show that the Evans function for the Euler-Poisson system converges to that for the Korteweg-de Vries (KdV) equation as an amplitude parameter tends to zero, from which we deduce that the origin is the only eigenvalue on its natural domain with algebraic multiplicity two. We also show that the solitary waves are spectrally stable in $L^2$ space. Moreover, we discuss (in)stability of large amplitude solitary waves.
