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