Some properties of small perturbations against a stationary solution of the nonlinear Schrodinger equation

被引:2
|
作者
Smolyakov, Mikhail N. [1 ,2 ]
机构
[1] Lomonosov Moscow State Univ, Skobeltsyn Inst Nucl Phys, Moscow 119991, Russia
[2] Russian Acad Sci, Inst Nucl Res, 60th October Anniversary Prospect 7a, Moscow 117312, Russia
基金
俄罗斯科学基金会;
关键词
Nonlinear Schrodinger equation; Gross-Pitaevskii equation; Nonlinear perturbations; Stationary solutions; Solitons; SOLITONS; VORTEX;
D O I
10.1016/j.chaos.2019.109570
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, classical small perturbations against a stationary solution of the nonlinear Schrodinger equation with the general form of nonlinearity are examined. It is shown that in order to obtain correct (in particular, conserved over time) nonzero expressions for the basic integrals of motion of a perturbation even in the quadratic order in the expansion parameter, it is necessary to consider nonlinear equations of motion for the perturbations. It is also shown that, despite the nonlinearity of the perturbations, the additivity property is valid for the integrals of motion of different nonlinear modes forming the perturbation (at least up to the second order in the expansion parameter). (C) 2019 Elsevier Ltd. All rights reserved.
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页数:8
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