Exact solution of the cubic-quintic Duffing oscillator

In this paper, we derive the exact solution of the cubic-quintic Duffing oscillator based on the use of Jacobi elliptic functions. We also showed that the exact angular frequency of this cubic-quintic Duffing equation is given in terms of the complete elliptic integral of the first kind.

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Bibliographic Details
Published in:Applied mathematical modelling 2013-02, Vol.37 (4), p.2574-2579
Main Author: Elías-Zúñiga, Alex
Format: Article
Language:English
Subjects:
Cubic-quintic nonlinear Schrödinger equation
Duffing equation
Duffing oscillators
Elliptic functions
Elliptic integrals
Exact solution
Exact solutions
Jacobian elliptic functions
Mathematical analysis
Mathematical models
solitons
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Description
Summary:In this paper, we derive the exact solution of the cubic-quintic Duffing oscillator based on the use of Jacobi elliptic functions. We also showed that the exact angular frequency of this cubic-quintic Duffing equation is given in terms of the complete elliptic integral of the first kind.
ISSN:0307-904X
DOI:10.1016/j.apm.2012.04.005