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Abstract
In order to study the uniformly translating solution of some non-linear evolution equations such as the complex Ginzburg---Landau equation, this paper presents a qualitative analysis to a Duffing---van der Pol non-linear oscillator. Monotonic property of the bounded exact solution is established based on the construction of a convex domain. Under certain parametric choices, one first integral to the Duffing---van der Pol non-linear system is obtained by using the Lie symmetry analysis, which constitutes one of the bases for further work of obtaining uniformly translating solutions of the complex Ginzburg---Landau equation.
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