Periodic Solutions of Modified Duffing Equation Subjected to Abi-Harmonic Parametric and External Excitations

Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...

Existence of Periodic Solutions for the Duffing Equation with Impulses

Chaotic dynamics of a Rayleigh-Duffing oscillator with periodically external and parametric excitations*

Chaotic motions of a Rayleigh-Duffing oscillator with periodically external and parametric excitations are investigated rigorously. Chaos arising from intersections of homoclinic orbits is analyzed with the Melnikov method. The critical curves separating the chaotic and non-chaotic regions are obtained. The chaotic feature on the system parameters is discussed. Chaotic dynamics are also compare...

periodic solutions of the duffing harmonic oscillator by he's energy balance method

duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...

Explicit multiple singular periodic solutions and singular soliton solutions to KdV equation

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...