Using the ZA method proposed for the first time in this paper, it is theoretically possible to
obtain general or analytical solutions for an infinite number of ordinary and partial differential …

Nonlinear second-order ordinary differential equations are common in various fields of
science, such as physics, mechanics and biology. Here we provide a new family of …

The problem of Liouvillian integrability for the classical force-free generalized Duffing
oscillators is solved completely. All the cases when the generalized Duffing oscillators …

We consider a family of nonlinear oscillators with quadratic damping, that generalizes the
Liénard equation. We show that certain nonlocal transformations preserve autonomous …

We provide the necessary and sufficient conditions of Liouvillian integrability for Liénard
differential systems describing nonlinear oscillators with a polynomial damping and a …

We propose a new class of nonlinear resonance networks which are modeled by standard
second-order nonlinear differential equations of the Levinson-Smith type or its subset, the …

In this work we study integrability of a family of nonlinear oscillators with linear and quadratic
damping. Equations from this family often appear in various applications in physics …

It is well known that the system of ordinary differential equations (ODEs) describing geodesic
flows of some Riemannian metrics on 2-surfaces admits a projection on a special class of …

The paper considers the possible relationship between the local integrability of an
autonomous two-dimensional ODE system with polynomial right hand sides and its global …

In this work, we re-visit third-order RLC resonance networks depicting the set of four basic
series and parallel resonance circuits where two circuits are admittance based (parallel …