I will sketchily illustrate how the theory of symmetry helps in determining solutions of
(deterministic) differential equations, both ODEs and PDEs, staying within the classical …

A Lie system is a time-dependent system of differential equations describing the integral
curves of a time-dependent vector field that can be considered as a curve in a finite …

Abstract We study Lie–Hamilton systems on the plane, ie systems of first-order differential
equations describing the integral curves of a t-dependent vector field taking values in a finite …

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 Lie system is a non-autonomous system of first-order differential equations possessing a
superposition rule, ie a map expressing its general solution in terms of a generic finite family …

Abstract A Lie–Hamilton (LH) system is a nonautonomous system of first-order ordinary
differential equations describing the integral curves of a t-dependent vector field taking …

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 …

This work presents a comprehensive review of the $ k $-polysymplectic Marsden-Weinstein
reduction theory, rectifying prior errors and inaccuracies in the literature while introducing …

A Lie system is a system of differential equations admitting a superposition rule, ie, a
function describing its general solution in terms of any generic set of particular solutions and …

In a recent paper (Nakamura and Martinez, 2019), the classical epidemic compartmental
susceptible‐infectious‐susceptible (SIS) model has been upgraded to a form which permits …