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

A reality weak nonlinear coupled two-dimensional system is constructed firstly by using coupling spring with variable force constant, the first order approximate Lie symmetries and approximate conserved quantities of the system are studied, 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.