Liapunov stability of generalized Langmuir solitons
- 1 January 1980
- journal article
- research article
- Published by AIP Publishing in Physics of Fluids
- Vol. 23 (1) , 44-51
- https://doi.org/10.1063/1.862861
Abstract
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 Schrödinger 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.Keywords
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