A nonconvex dissipative system and its applications (I)

Authors:
Zhaosheng Feng
Affiliations:
Department of Mathematics, University of Texas---Pan American, Edinburg, USA 78541
Venue:
Journal of Global Optimization
Year:
2008

Citing 7
Cited 0

Nonlinear ordinary differential equations (2nd ed.)

Nonlinear ordinary differential equations (2nd ed.)
Duality in stochastic linear and dynamic programming

Duality in stochastic linear and dynamic programming
Fronts, pulses, sources and sinks in generalized complex Ginzberg-Landau equations

Physica D
An alternative analysis of Duffing's equation

SIAM Review
The qualitative analysis of a dynamical system modeling the formation of multilayer scales on pure metals

SIAM Journal on Mathematical Analysis
Engineering and Economic Applications of Complementarity Problems

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Complementarity: Applications, Algorithms and Extensions (Applied Optimization)

Complementarity: Applications, Algorithms and Extensions (Applied Optimization)

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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.