A nonconvex dissipative system and its applications (I) |
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| Authors: | Zhaosheng Feng |
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| Affiliation: | (1) Department of Mathematics, University of Texas–Pan American, Edinburg, TX 78541, USA |
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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. Dedicated to Professor G. Strang on the occasion of his 70th birthday |
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| Keywords: | Ginzburg– Landau equation Autonomous system First integral Oscillator Equilibrium point Lie symmetry |
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