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弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量

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楼智美, 梅凤翔, 陈子栋. 2012: 弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量, 物理学报, 61(11): 41-45.
引用本文: 楼智美, 梅凤翔, 陈子栋. 2012: 弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量, 物理学报, 61(11): 41-45.
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2012: The first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator, Acta Physica Sinica, 61(11): 41-45.
Citation: 2012: The first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator, Acta Physica Sinica, 61(11): 41-45.
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弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量

  • 绍兴文理学院物理系,绍兴,312000

  • 北京理工大学力学系,北京,100081

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

  • 摘要: 用近似Lie对称性理论研究弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量，并以频率比为2：l的弱非线性耦合二维各向异性谐振子为例，得到其6个一阶近似Lie对称性和一阶近似守恒量，其中1个一阶近似守恒量实为系统的精确守恒量，4个一阶近似守恒量为平凡的一阶近似守恒量，只有1个一阶近似守恒量为稳定的一阶近似守恒量．
    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 ω1/ω2 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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  • 刊出日期:  2012-06-15

弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量

  • 绍兴文理学院物理系,绍兴,312000
  • 北京理工大学力学系,北京,100081

摘要: 用近似Lie对称性理论研究弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量，并以频率比为2：l的弱非线性耦合二维各向异性谐振子为例，得到其6个一阶近似Lie对称性和一阶近似守恒量，其中1个一阶近似守恒量实为系统的精确守恒量，4个一阶近似守恒量为平凡的一阶近似守恒量，只有1个一阶近似守恒量为稳定的一阶近似守恒量．

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