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Asymptotic localization of stationary states in the nonlinear Schroedinger equation

机译：非线性系统中静态的渐近定位 schroedinger方程

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摘要

The mapping of the Nonlinear Schroedinger Equation with a random potential onthe Fokker-Planck equation is used to calculate the localization length of itsstationary states. The asymptotic growth rates of the moments of the wavefunction and its derivative for the linear Schroedinger Equation in a randompotential are computed analytically and resummation is used to obtain thecorresponding growth rate for the nonlinear Schroedinger equation and thelocalization length of the stationary states.

机译：在Fokker-Planck方程上将具有随机势的非线性Schroedinger方程映射用于计算其平稳状态的定位长度。分析了随机势中线性Schroedinger方程的波动函数矩及其导数的渐近增长率，并利用求和法求出了非线性Schroedinger方程的相应增长率和稳态的定域长度。

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Fishman, Shmuel; Iomin, Alexander; Mallick, Kirone;
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年度 2008
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2. Long-time asymptotics for the defocusing integrable discrete nonlinear Schroedinger equation [J] . Hideshi Yamane Journal of the Mathematical Society of Japan . 2014,第3期

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3. EXISTENCE AND UNIQUENESS OF SINGULAR SOLUTION TO STATIONARY SCHROEDINGER EQUATION WITH SUPERCRITICAL NONLINEARITY [J] . Fouad Hadj Selem, Hiroaki Kikuchi, Juncheng Wei Discrete and continuous dynamical systems . 2013,第10期

机译：具超临界非线性的Scheedinger方程的奇异解的存在性和唯一性
4. Asymptotically symplectic integrators of 3rd and 4th order for the numerical solution of the Schroedinger equation [C] . Z. Kalogiratou, Th. Monovasilis, T.E. Simos Massachusetts Institute of Technology(MIT) Conference on Computational Fluid and Solid Mechanics 2003 v.2; 20030617-20030620; Cambridge,MA; US . 2003

机译：Schroedinger方程数值解的三阶和四阶渐近辛积分
5. Nonlinear Schroedinger-type equations with asymptotically linear terms. [D] . van Heerden, Francois Alwyn. 2002

机译：具有渐近线性项的非线性Schroedinger型方程。
6. Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy–Sobolev exponent and singular nonlinearity [O] . Liejun Shen -1

机译：具有Hardy-Sobolev指数和奇异非线性的Kirchhoff型方程解的多重性和渐近性
7. Existence of dark solitons in a class of stationary nonlinear Schrödinger equations with periodically modulated nonlinearity and periodic asymptotics [O] . Belmonte-Beitia Juan, Cuevas-Maraver Jesús 2011

机译：一类具有周期调制非线性和周期渐近性的平稳非线性薛定ding方程中暗孤子的存在
8. Some Remarks on the Asymptotic Behaviour of Solutions to Nonlinear Schroedinger Equations [R] . Cazenave, T. 1984

机译：关于非线性schroedinger方程解的渐近性的一些注记

Asymptotic localization of stationary states in the nonlinear Schroedinger equation

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