Liapunov stability of generalized Langmuir solitons
Liapunov stability of generalized Langmuir solitons
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DOI：
10.1063/1.862861
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发表时间：
1980
影响因子：
4.6
通讯作者：
E. Laedke;K. Spatschek
中科院分区：
文献类型：
--
作者：
E. Laedke;K. Spatschek
将小振幅朗缪尔孤子的稳定性研究推广到有限振幅孤立波。以前对朗缪尔包络孤子稳定性的考虑是基于立方非线性薛定谔方程或所谓的扎哈罗夫方程。因此，它们仅在弱非线性区域有效。为了讨论有限振幅孤立波的纵向稳定性，必须考虑更一般的低频响应。以完全非线性离子方程为例，研究了有限振幅孤立波的稳定性。该方法是完全非线性的，并利用李雅普诺夫理论。给出了一个稳定性判据，证明了已知驻波解的纵向稳定性。横向不稳定性的作用进行了讨论。
The stability investigations for small amplitude Langmuir solitons are generalized to finite amplitude solitary waves. Previous stability considerations for Langmuir envelope solitons are based on the cubic nonlinear Schrodinger equation or the so‐called Zakharov equations. Thus, they are only valid in the weakly nonlinear regime. To discuss the longitudinal stability of finite amplitude solitary waves a more general low‐frequency response has to be allowed for. Taking the full nonlinear ion equations, the stability behavior of finite amplitude solitary waves is investigated. The method is completely nonlinear and makes use of Liapunov theory. A stability criterion is derived which proves the longitudinal stability for the known stationary wave solutions. The role of transverse instabilities is also discussed.