Lie systems form a class of systems of first-order ordinary differential equations whose
general solutions can be described in terms of certain finite families of particular solutions …

This work concerns the definition and analysis of a new class of Lie systems on Poisson
manifolds enjoying rich geometric features: the Lie–Hamilton systems. We devise methods …

A class of exact solutions is obtained for the Liénard-type ordinary nonlinear differential
equation. As a first step in our study, the second-order Liénard-type equation is transformed …

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

WEIERSTRASS INTEGRABILITY IN LIÉNARD DIFFERENTIAL SYSTEMS 1. Introduction
We consider the Liénard differential equations of th Page 1 WEIERSTRASS …

A superposition rule is a particular type of map that enables one to express the general
solution of certain systems of first-order ordinary differential equations, the so-called Lie …

In this work we suggest a systematic method of construction of solutions of the n-order
Riccati equation with constant coefficients in a field from the set of generalized trigonometric …

This work presents a newly renovated approach to the analysis of second-order Riccati
equations from the point of view of the theory of Lie systems. We show that these equations …

The Riccati polynomial differential systems are differential systems of the form x′= c 0 (x),
y′= b 0 (x)+ b 1 (x) y+ b 2 (x) y 2, where c 0 and bi for i= 0, 1, 2 are polynomial functions. We …

For Liénard systems x˙= y, y˙=− fm (x) y− gn (x) with fm and gn real polynomials of degree m
and n respectively, in [H. Zoladek, Algebraic invariant curves for the Liénard equation, Trans …