Reductions for systems of ODEs integrable via the standard factorization method (the Adler-
Kostant-Symes scheme) or the generalized factorization method, developed by the authors …

The PT is applied to the general second-and third-order ordinary differential equations
invariant under the two symmetries associated with time translation and rescaling in order to …

In this paper, we demonstrate that the modified equation of Emden type (MEE),, is integrable
either explicitly or by quadrature for any value of α and β. We also prove that the MEE …

We apply the Darboux theory to study the integrability of real quadratic differential systems
having an invariant conic. The fact that two intersecting straight lines or two parallel straight …

We modified the classical SIR model of Kermack and McKendrick by assuming that an
individual can be born infected. We analysed the model from the point of view of symmetry …

Abstract The Emden-Fowler equation of index n is studied utilising the techniques of Lie and
Painlevé analysis. For general n information about the integrability of this equation is …

We present a method to construct superintegrable n-component Lotka–Volterra (LV)
systems with $3 n-2$ parameters. We apply the method to LV systems with n components for …

The general solutions of many three-dimensional Lotka–Volterra systems, previously known
to be at least partially integrable, are constructed with the aid of special functions. Examples …

Any singular irreducible cubic curve (or simply, cubic) after an affine transformation can be
written as either y 2= x 3, or y 2= x 2 (x+ 1), or y 2= x 2 (x− 1). We classify the phase portraits …

Let P and Q be real homogeneous polynomials in the variables x and y of degrees m and n
respectively. Then we say that X=(P, Q): RZ--t R2 is a semi-homogeneous polynomial vector …