The Non-linear Schrödinger Equation and the Conformal Properties of Non-relativistic Space-Time

被引：0
作者：
P. A. Horváthy
J.-C. Yera
机构：
[1] Université de Tours,Laboratoire de Mathématiques et de Physique Théorique
来源：
International Journal of Theoretical Physics | 2009年 / 48卷
关键词：
Non-linear Schrödinger equation; Schrödinger symmetry; Conformal structure of non-relativistic space-time;
D O I：
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学科分类号：
摘要：
The cubic non-linear Schrödinger equation where the coefficient of the nonlinear term is a function F(t,x) only passes the Painlevé test of Weiss, Tabor, and Carnevale only for F=(a+bt)−1, where a and b are constants. This is explained by transforming the time-dependent system into the constant-coefficient NLS by means of a time-dependent non-linear transformation, related to the conformal properties of non-relativistic space-time. A similar argument explains the integrability of the NLS in a uniform force field or in an oscillator background.
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页码：3139 / 3146
页数：7
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