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

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

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2:1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.

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.