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The first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator

Lou Zhi-Mei Mei Feng-Xiang Chen Zi-Dong

The first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator

Lou Zhi-Mei, Mei Feng-Xiang, Chen Zi-Dong
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  • Received Date:  30 July 2011
  • Accepted Date:  04 June 2012
  • Published Online:  05 June 2012

The first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator

  • 1. Department of Physics, Shaoxing University, Shaoxing 312000, China;
  • 2. Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China
Fund Project:  Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 10932002).

Abstract: The first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator are studied. When the 1/2 is equal to 2/1, the system possesses six first-order approximate Lie symmetries and approximate conserved quantities, one of them is an exact conserved quantity, four of them are trivial conserved quantities, only one of them is a stable conserved quantity.

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