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：
暂无
中图分类号：
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.
引用
收藏
页码：3139 / 3146
页数：7
相关论文
共 50 条
  • [1] The Non-linear Schrodinger Equation and the Conformal Properties of Non-relativistic Space-Time
    Horvathy, P. A.
    Yera, J. -C.
    [J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2009, 48 (11) : 3139 - 3146
  • [2] THE NON-RELATIVISTIC SPACE-TIME MANIFOLDS
    KAPUSCIK, E
    [J]. ACTA PHYSICA POLONICA B, 1981, 12 (02): : 81 - 86
  • [3] Instability for the Semiclassical Non-linear Schrödinger Equation
    Nicolas Burq
    Maciej Zworski
    [J]. Communications in Mathematical Physics, 2005, 260 : 45 - 58
  • [4] On the variational principle for the non-linear Schrödinger equation
    Zsuzsanna É. Mihálka
    Ádám Margócsy
    Ágnes Szabados
    Péter R. Surján
    [J]. Journal of Mathematical Chemistry, 2020, 58 : 340 - 351
  • [5] The non-linear Schrödinger equation with a periodic δ-interaction
    Jaime Angulo Pava
    Gustavo Ponce
    [J]. Bulletin of the Brazilian Mathematical Society, New Series, 2013, 44 : 497 - 551
  • [6] Destruction of the Beating Effect¶for a Non-Linear Schrödinger Equation
    Vincenzo Grecchi
    André Martinez
    Andrea Sacchetti
    [J]. Communications in Mathematical Physics, 2002, 227 : 191 - 209
  • [7] Non-linear Schrödinger equation with non-local regional diffusion
    Patricio Felmer
    César Torres
    [J]. Calculus of Variations and Partial Differential Equations, 2015, 54 : 75 - 98
  • [8] ON THE SPACE-TIME FORMULATION OF NON-RELATIVISTIC QUANTUM MECHANICS
    FUJIWARA, I
    [J]. PROGRESS OF THEORETICAL PHYSICS, 1959, 21 (06): : 902 - 918
  • [9] SPACE-TIME APPROACH TO NON-RELATIVISTIC QUANTUM MECHANICS
    FEYNMAN, RP
    [J]. REVIEWS OF MODERN PHYSICS, 1948, 20 (02) : 367 - 387
  • [10] Localization in the Discrete Non-linear Schrödinger Equation and Geometric Properties of the Microcanonical Surface
    Claudio Arezzo
    Federico Balducci
    Riccardo Piergallini
    Antonello Scardicchio
    Carlo Vanoni
    [J]. Journal of Statistical Physics, 2022, 186
12345