Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications

The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly by obtaining the period and the solution. The period is given in terms of the complete elliptic integral of the first kind and the solut...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2022-01, Vol.2022 (1)
Main Authors: Salas, Alvaro H., Martínez H, Lorenzo J., Ocampo R, David L.
Format: Article
Language:English
Subjects:
Algebra
Approximation
Duffing equation
Duffing oscillators
Exact solutions
Initial conditions
Jacobian elliptic functions
Nonlinear differential equations
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Summary:The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly by obtaining the period and the solution. The period is given in terms of the complete elliptic integral of the first kind and the solution involves Jacobian elliptic functions. We solve the cubic-quintic Duffing equation under arbitrary initial conditions. Physical applications are provided. The solution to the mixed parity Duffing oscillator is also formally derived. We illustrate the obtained results with concrete examples. We give high accurate trigonometric approximations to the Jacobian function cn.
ISSN:1076-2787
1099-0526
DOI:10.1155/2022/9269957