Parametric autoresonant excitation of the nonlinear Schrodinger equation

被引：5
|
作者：
Friedland, L. [1 ]
Shagalov, A. G. [2 ,3 ]
机构：
[1] Hebrew Univ Jerusalem, Racah Inst Phys, IL-91904 Jerusalem, Israel
[2] Inst Met Phys, Ekaterinburg 620990, Russia
[3] Ural Fed Univ, Mira 19, Ekaterinburg 620002, Russia
来源：
PHYSICAL REVIEW E | 2016年 / 94卷 / 04期
基金：
以色列科学基金会;
关键词：
SOLITONS; WAVE;
D O I：
10.1103/PhysRevE.94.042216
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：
Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the driving wave for entering the autoresonant regime. It is shown that above the threshold, a flat (spatially independent) NLS solution can be fully converted into a traveling wave. A simplified, few spatial harmonics expansion approach is also developed for studying this nonlinear mode conversion process, allowing interpretation as autoresonant interaction within triads of spatial harmonics.
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收藏
页数：10
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