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A nonconvex dissipative system and its applications (I)

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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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  1. Department of Mathematics, University of Texas–Pan American, Edinburg, TX, 78541, USA

    Zhaosheng Feng

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  1. Zhaosheng Feng
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Correspondence to Zhaosheng Feng.

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Dedicated to Professor G. Strang on the occasion of his 70th birthday

The work has been presented at the International Conference on Complementarity, Duality, and Global Optimization in Science and Engineering, Virginia Tech. University, Blacksburg, Virginia, August 15–17, 2005. The author would like to thank the organizers Professors David Y. Gao and Hanif D. Sherali for their generous support. This work is partly supported by NSF Grant CCF–0514768.

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Feng, Z. A nonconvex dissipative system and its applications (I). J Glob Optim 40, 623–636 (2008). https://doi.org/10.1007/s10898-006-9115-z

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