Exact solutions of the cubic-quintic Duffing equation using leaf functions

Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation

In this paper, based on a combination of homogenous balance and the rational expansion method, the exact analytical and closed-form solutions of the Duffing equation with cubic and quintic nonlinearities are derived. We focus on heteroclinic and homoclinic solutions which are relevant for the prediction of chaos in forced mechanical systems. The conditions of existence of these solutions which ...

Analytical Approximate Solutions for the Cubic-Quintic Duffing Oscillator in Terms of Elementary Functions

1 Departamento de Fı́sica, Ingenierı́a de Sistemas y Teorı́a de la Señal, Universidad de Alicante, Apartado 99, 03080 Alicante, Spain 2 Instituto Universitario de Fı́sica Aplicada a las Ciencias y las Tecnologı́as, Universidad de Alicante, Apartado 99, 03080 Alicante, Spain 3 Departamento de Ciencias Médicas, Facultad de Medicina, Universidad de Castilla-La Mancha, C/Almansa No. 14, 02006 Albacete, ...

Duffing equations with cubic and quintic nonlinearities

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...

Exact solutions of the cubic–quintic Swift–Hohenberg equation and their bifurcations

Exact localized Solutions of Quintic Discrete Nonlinear Schrödinger Equation

We study a new quintic discrete nonlinear Schrödinger (QDNLS) equation which reduces naturally to an interesting symmetric difference equation of the form φn+1+ φn−1 = F (φn). Integrability of the symmetric mapping is checked by singularity confinement criteria and growth properties. Some new exact localized solutions for integrable cases are presented for certain sets of parameters. Although t...