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A real weak nonlinear coupled two-dimensional system is constructed first 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, of which one is an exact conserved quantity, four are trivial conserved quantities, and only one is a stable conserved quantity.
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Keywords:
- weak nonlinear coupled two-dimensional system/
- approximate Lie symmetries/
- approximate conserved quantity
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