The Duffing oscillator of a system with strong quadratic damping is considered. We give an
elementary approximate analytical solution to this oscillator in terms of exponential and …

We have examined a class of Liénard–Levinson–Smith (LLS) oscillators having a stable
limit cycle which demonstrates the fact that the LLS theorem can only be applied under an …

We propose a geometric integrator to numerically approximate the flow of Lie systems. The
key is a novel procedure that integrates the Lie system on a Lie group intrinsically …

In this paper, the large-amplitude oscillation of a triple-well non-natural system, covering
both qualitative and quantitative analysis, is investigated. The nonlinear system is governed …

The Lambert W function has utility for solving various exponential and logarithmic equations
arranged in the form of $ g (x) e^{g (x)} $. Using the Lambert W function and tetration, a …

Quadratically damped oscillators with non-linear restoring force arXiv:1610.07821v1 [nlin.CD] 25
Oct 2016 Page 1 Quadratically damped oscillators with non-linear restoring force Ankan …

We consider a nonlinear generalization of the isotonic oscillator with an asymmetric
potential.(2) Using a symmetrization principle we construct a symmetric potential.(3) The …

A Lie system is a nonautonomous system of first-order ordinary differential equations whose
general solution can be written via an autonomous function, the so-called (nonlinear) …

Oscillators with a Duffing-type restoring force and quadratic damping are dealt with in this
paper. Four characteristic cases of this restoring force are analysed: hardening, softening …

We have examined a class of Li\'enard--Levinson--Smith (LLS) system having a stable limit
cycle which demonstrates the case where the LLS theorem cannot be applied. The problem …