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．%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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