Guangyue Gao, Zhaosheng Feng
Abstract:
In this article, under certain parametric conditions,
we study the first integrals of the Duffing-van der Pol-type
oscillator equations which include the van der Pol and the
Duffing oscillator systems, as particular cases.
After making a series of variable transformations and applying
the Preller-Singer method, we find the first integrals of the
simplified equations without complicated calculations.
Through the inverse transformations we obtain the first
integrals of the original equations. Some statements in the
literature are indicated and clarified.
Published September 25, 2010.
Math Subject Classifications: 34A25, 34L30.
Key Words: First integral; Duffing oscillator; van der Pol oscillator;
Preller-Singer method; parametric solution.
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Guangyue Gao Department of Mathematics, University of Texas-Pan American Edinburg, TX 78539, USA email: gygao@broncs.utpa.edu | |
Zhaosheng Feng Department of Mathematics, University of Texas-Pan American Edinburg, TX 78539, USA email: zsfeng@utpa.edu fax: 956-381-5091 |
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