Reduction of time-dependent systems admitting a superposition principle

被引：40
|
作者：
Cariñena, JF [1 ]
Grabowski, J [1 ]
Ramos, A [1 ]
机构：
[1] Univ Zaragoza, Dept Fis Teor, E-50009 Zaragoza, Spain
来源：
ACTA APPLICANDAE MATHEMATICAE | 2001年 / 66卷 / 01期
关键词：
nonlinear superposition; time-dependent systems; equations on Lie groups; Lie reduction theory;
D O I：
10.1023/A:1010743114995
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The problem of differential equation systems admitting a nonlinear superposition principle is analyzed from a geometric perspective. We show how it is possible to reduce the problem of finding the general solution of such a differential equation system defined by a Lie group G to a pair of simpler problems, one in a subgroup H and the other on a homogeneous space. The theory is illustrated with several examples and applications.
引用
收藏
页码：67 / 87
页数：21
相关论文
共 50 条
  • [21] Problem-free time-dependent variational principle for open quantum systems
    Joubert-Doriol, Loic
    Izmaylov, Artur F.
    JOURNAL OF CHEMICAL PHYSICS, 2015, 142 (13):
  • [22] Time-Dependent Variational Principle for Open Quantum Systems with Artificial Neural Networks
    Reh, Moritz
    Schmitt, Markus
    Gaerttner, Martin
    PHYSICAL REVIEW LETTERS, 2021, 127 (23)
  • [23] TIME-DEPENDENT VARIATIONAL PRINCIPLE AND THE EFFECTIVE ACTION
    JACKIW, R
    KERMAN, A
    PHYSICS LETTERS A, 1979, 71 (2-3) : 158 - 162
  • [24] Time-Dependent Variational Principle for Quantum Lattices
    Haegeman, Jutho
    Cirac, J. Ignacio
    Osborne, Tobias J.
    Pizorn, Iztok
    Verschelde, Henri
    Verstraete, Frank
    PHYSICAL REVIEW LETTERS, 2011, 107 (07)
  • [25] Time-dependent variational principle for dissipative dynamics
    Kraus, Christina V.
    Osborne, Tobias J.
    PHYSICAL REVIEW A, 2012, 86 (06):
  • [26] SOME COMMENTS ON TIME-DEPENDENT VARIATION PRINCIPLE
    LOWDIN, PO
    MUKHERJEE, PK
    CHEMISTRY AND PHYSICS OF LIPIDS, 1972, 14 (01) : 1 - +
  • [27] ON A VARIATIONAL PRINCIPLE FOR TIME-DEPENDENT SCHRODINGER EQUATION
    PRAT, R
    MOLECULAR PHYSICS, 1967, 13 (02) : 193 - &
  • [28] VARIATIONAL PRINCIPLE FOR TIME-DEPENDENT SCHRODINGER EQUATION
    GURTIN, ME
    JOURNAL OF MATHEMATICAL PHYSICS, 1965, 6 (10) : 1506 - &
  • [29] Experimental demonstration of classical analogous time-dependent superposition of states
    Mahmood, Kazi T.
    Hasan, M. Arif
    SCIENTIFIC REPORTS, 2022, 12 (01)
  • [30] Experimental demonstration of classical analogous time-dependent superposition of states
    Kazi T. Mahmood
    M. Arif Hasan
    Scientific Reports, 12
12345