Here we present a new approach to compute symmetries of rational second order ordinary
differential equations (rational 2ODEs). This method can compute Lie symmetries (point …

It is investigated how two (standard or generalized)-symmetries of a given second-order
ordinary differential equation can be used to solve the equation by quadratures. The method …

Here we present a new approach to search for first order invariants (first integrals) of rational
second order ordinary differential equations. This method is an alternative to the Darbouxian …

Constants of motion, Lagrangians, and Hamiltonians admitted by a family of relevant
nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last …

Here we present an efficient method for finding and using a nonlocal symmetry admitted by
a rational second order ordinary differential equation (rational 2ODE) in order to find a …

After the introduction of λ-symmetries by Muriel and Romero, several other types of so called
“twisted symmetries” have been considered in the literature (their name refers to the fact they …

We introduce a new local transformation that connects certain hierarchies of ODEs with the
Riccati chain. Such transformation is derived from the existence of a common λ-symmetry for …

We propose a new symmetry reduction method for (1+ 1)-dimensional differential-difference
equations (DDEs), namely, the λ-symmetry reduction method of solving ordinary differential …

Abstract In Duarte et al.(2016) and Avellar et al.(2019), we have developed a method (we
call it S-function method) that is successful in treating certain classes of rational second …

For ordinary differential equations, the genesis of the concept of C https://s3-euw1-ap-pe-df-
pch-content-public-p. s3. eu-west-1. amazonaws. com/9780429263743/15e65f54-7536 …