The extended Prelle-Singer method for the conserved quantities of second-ordinary nonlinear coupled dynamics systems and their symmetries

被引：6
|
作者：
Lou Zhi-Mei [1 ]
机构：
[1] Shaoxing Univ, Dept Phys, Shaoxing 312000, Peoples R China
来源：
ACTA PHYSICA SINICA | 2010年 / 59卷 / 02期
关键词：
extended Prelle-Singer method; second-ordinary nonlinear coupled dynamics systems; conserved quantity; symmetry; ORDINARY DIFFERENTIAL-EQUATIONS; MEI SYMMETRY; LIE SYMMETRY; CONSTRUCTION; INVARIANTS; INTEGRALS; PARTICLE;
D O I：
10.7498/aps.59.719
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The extended Prelle-Singer method is used to find the conserved quantities of second-ordinary nonlinear coupled dynamics systems such as (x) over dot = phi(1) (x, y) (y) over dot = phi(2) (x, y), and the differential equations of integral factors and the general expression of conserved quantities are obtained. The Noether symmetry and Lie symmetry of the systems are also discussed. Finally,two conserved quantities of quartic anharminic oscillator are obtained by the extended Prelle-Singer method,and the symmetries of this system are discussed.
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收藏
页码：719 / 723
页数：5
相关论文
共 28 条
  • [1] Annamalai A, 1994, NONLINEAR MATH PHYS, V1, P309
  • [2] A simple and unified approach to identify integrable nonlinear oscillators and systems
    Chandrasekar, VK
    Pandey, SN
    Senthilvelan, M
    Lakshmanan, M
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (02)
  • [3] A unification in the theory of linearization of second-order nonlinear ordinary differential equations
    Chandrasekar, VK
    Senthilvelan, M
    Lakshmanan, M
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (03): : L69 - L76
  • [4] Extended Prelle-Singer method and integrability/solvability of a class of nonlinear nth order ordinary differential equations
    Chandrasekar V.K.
    Senthilvelan M.
    Lakshmanan M.
    [J]. Journal of Nonlinear Mathematical Physics, 2005, 12 (Suppl 1) : 184 - 201
  • [5] Analysing the structure of the integrating factors for first-order ordinary differential equations with Liouvillian functions in the solution
    Duarte, LGS
    Duarte, SES
    da Mota, LACP
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2002, 35 (04): : 1001 - 1006
  • [6] Solving second-order ordinary differential equations by extending the Prelle-Singer method
    Duarte, LGS
    Duarte, SES
    da Mota, LACP
    Skea, JEF
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (14): : 3015 - 3024
  • [7] New conserved quantities of Noether-Mei symmetry of mechanical system in phase space
    Fang Jian-Hui
    Liu Yang-Kui
    Zhang Xiao-Ni
    [J]. CHINESE PHYSICS B, 2008, 17 (06) : 1962 - 1966
  • [8] Fang JH, 2007, CHINESE PHYS, V16, P887, DOI 10.1088/1009-1963/16/4/002
  • [9] Ge W K, 2001, ACTA ARMAMENTARII, P22
  • [10] Mei symmetry and conserved quantity of a holonomic system
    Ge Wei-Kuan
    [J]. ACTA PHYSICA SINICA, 2008, 57 (11) : 6714 - 6717
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