EXACT SOLUTIONS TO CUBIC DUFFING EQUATION FOR A NONLINEAR ELECTRICAL CIRCUIT
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Universidad Distrital Francisco José de Caldas
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This work provides an exact solution to a cubic Duffing oscillator equation with initial conditions and bounded periodic solutions. This solution is expressed in terms of the Jacobi elliptic function (cn). This exact solution is used as a seed to give a good analytic approximate solution to a nonlinear equation that describes a nonlinear electrical circuit. This last equation is solved numerically and compared with the analytic solution obtained from solving the cubic Duffing equation. It is suggested that the methodology used herein may be useful in the study of other nonlinear problems described by differential equations of the form z ΠΠ= F(z) , F(z) being an odd function in the sense thaFt (z) may be approximated by an appropriate solution to a cubic Duffing oscillator equation. In particular, the exact solution may be applied in the study of the cubic nonlinear Schrodinger equation, which is reduced to a cubic Duffing oscillator equation by means of a travelling wave transformation.
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Duffing equation, cubic Duffing oscillator equation, third-order Duffing model, analytic solution, Jacobi elliptic functions.