非线性薛定谔方程理论中暗孤子运动的哈密顿理论

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
A. M. Kamchatnov
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引用次数: 0

摘要

摘要 我们开发了一种方法来推导汉密尔顿方程,该方程描述了当孤子沿着非均质且时变的大尺度背景运动时,非线性波方程在阿布洛维茨-考普-纽维尔-塞古尔(AKNS)方案中的完全可积分性。该方法基于老斯托克斯思想的发展,允许将线性波的分析关系延续到孤子区域,并在离焦非线性薛定谔方程的例子中得到了实际应用。我们提出了一个条件,即只有在描述背景演变时才考虑外部电势,在这种情况下,就可以得到外部电势中的孤子动力学牛顿方程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hamiltonian theory of motion of dark solitons in the theory of nonlinear Schrödinger equation

We develop a method for deriving Hamilton’s equations describing the dynamics of solitons when they move along an inhomogeneous and time-varying large-scale background for nonlinear wave equations that are completely integrable in the Ablowitz–Kaup–Newell–Segur (AKNS) scheme. The method is based on the development of old Stokes’ ideas that allow analytically continuing the relations for linear waves into the soliton region, and is practically implemented in the example of the defocusing nonlinear Schrödinger equation. A condition is formulated under which the external potential is only to be taken into account when describing the evolution of the background, and that this case, the Newton equation is obtained for the soliton dynamics in an external potential.

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来源期刊
Theoretical and Mathematical Physics
Theoretical and Mathematical Physics 物理-物理:数学物理
CiteScore
1.60
自引率
20.00%
发文量
103
审稿时长
4-8 weeks
期刊介绍: Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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