Exact solution of the quadratic mixed-parity Helmholtz-Duffing oscillator

DOI10.1016/j.amc.2012.01.025zbMath1245.34002OpenAlexW2059708904MaRDI QIDQ433309

Alex Elías-Zúñiga

Publication date: 13 July 2012

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2012.01.025

zbMATH Keywords

homoclinic bifurcationJacobian elliptic functionsnonlinear oscillatorasymmetric behaviormixed-parityquadratic nonlinearities

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Explicit solutions, first integrals of ordinary differential equations (34A05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items (11)

A new exact solution of a damped quadratic non-linear oscillator ⋮ Application of the elliptic balance method to a nonlinear singular oscillator ⋮ On the solution of strong nonlinear oscillators by applying a rational elliptic balance method ⋮ A new approach for modelling the damped Helmholtz oscillator: applications to plasma physics and electronic circuits ⋮ Enhanced multistage homotopy perturbation method: approximate solutions of nonlinear dynamic systems ⋮ Exact solutions for the quadratic mixed-parity Helmholtz-Duffing oscillator by bifurcation theory of dynamical systems ⋮ Analytical solution of the damped Helmholtz-Duffing equation ⋮ Exact solutions of a generalized autonomous Duffing-type equation ⋮ Closed-form exact solutions for the unforced quintic nonlinear oscillator ⋮ ANALYTICAL SOLUTION OF THE FRACTAL CUBIC–QUINTIC DUFFING EQUATION ⋮ EQUIVALENT POWER-FORM REPRESENTATION OF THE FRACTAL TODA OSCILLATOR

Cites Work

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• Analysis of a beam-column system under varying axial forces of elliptic type: The exact solution of Lamé's equation
• Symmetry-breaking analysis for the general Helmholtz-Duffing oscillator
• A RATIONAL HARMONIC BALANCE APPROXIMATION FOR THE DUFFING EQUATION OF MIXED PARITY
• Quadratic non-linear oscillators
• ON THE ELLIPTIC HARMONIC BALANCE METHOD FOR MIXED PARITY NON-LINEAR OSCILLATORS
• Solution of a quadratic nonlinear oscillator by the method of harmonic balance
• Exact solution of a quadratic nonlinear oscillator
• AN ELLIPTIC PERTURBATION METHOD FOR CERTAIN STRONGLY NON-LINEAR OSCILLATORS
• COMMENTS ON “A RATIONAL HARMONIC BALANCE APPROXIMATION FOR THE DUFFING EQUATION OF MIXED PARITY” (WITH AUTHORS' REPLY)
• A note on the Helmholtz oscillator

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