Dynamics of solitary waves in the Zakharov model equations

被引:61
作者
Malomed, B
Anderson, D
Lisak, M
QuirogaTeixeiro, ML
Stenflo, L
机构
[1] UMEA UNIV, DEPT PLASMA PHYS, S-90187 UMEA, SWEDEN
[2] TEL AVIV UNIV, SCH MATH SCI, DEPT APPL MATH, IL-69978 TEL AVIV, ISRAEL
关键词
D O I
10.1103/PhysRevE.55.962
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We analyze internal vibrations of a solitary wave in the generalized Zakharov system (including a direct nonlinear self-interaction of the high-frequency field) by means of a variational approach. The application of the variational approximation to this model turns out to be nontrivial, as one needs to renormalize the Lagrangian in order to avoid divergences. This is done with the use of two fundamental integrals of motion of the model. We derive a Hamiltonian two-degrees-of-freedom dynamical system that governs internal vibrations of the solitary wave. The eigenfrequencies of the small oscillations around the unperturbed solitary wave are found explicitly, one of them lying inside the gap of the high-frequency subsystem, the other one being well above the gap. Finite-amplitude oscillations are simulated numerically. It is shown that these oscillations remain regular if the perturbation does not break the balance between the two integrals of motion, while in the opposite case the oscillations are more irregular and may possibly become chaotic.
引用
收藏
页码:962 / 968
页数:7
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