Related papers: Third Order ODEs Systems and Its Characteristic Co…

Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on…

We explore the existence of a class of generalised Laplace maps for third order partial differential operators of the form…

Cartan's equivalence method is applied to explicitly construct invariant coframes for four branches, which are used to characterize all non-linearizable third-order ODEs with a four-dimensional Lie symmetry subalgebra under point…

Point transformations of the 3-rd order ordinary differential equations are considered. Special classes of ordinary differential equations that are invariant under the general point transformations are constructed.

Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of nonequivalent equations is issued. As the exampes the…

This paper considers a family of finite dimensional simple Lie superalgebras of Cartan type over a field of characteristic $p>3$, the so-called special odd contact superalgebras. First, the spanning sets are determined for the Lie…

We find the complete set of fundamental invariants for systems of ordinary differential equations of order $\ge 4$ under the group of point transformations generalizing similar results for contact invariants of a single ODE and point…

We compute all third-order local invariants accessible via randomised measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite…

Ordinary differential equations (ODEs) and ordinary difference systems (O$\Delta$Ss) invariant under the actions of the Lie groups $\mathrm{SL}_x(2)$, $\mathrm{SL}_y(2)$ and $\mathrm{SL}_x(2)\times\mathrm{SL}_y(2)$ of projective…

In this paper we define $n$th order Hessian structures on manifolds and study them. In particular, when $n = 3$, we make a detailed study and establish a one-to-one correspondence between {\it third-order Hessian structures} and a {\it…

These are lecture notes of the Summer school on the geometry of differential equations held in Nordfjordeid, Norway in 1996. They cover geometric structures related to scalar second order ODEs, the construction of the associated Cartan…

A novel family of integrable third order maps is presented. Each map possesses, by construction, a pair of rational invariants and a commuting map from the same class. The 3-dimensional invariant curve is parametrized, in general, by an…

A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of…

Let $dx_i/dt=f_i(x_1,\cdots,x_n)$, ($i=1,\cdots,n$) be a system of $n$ first order autonomous ordinary differential equations. We use E. Cartan's equivalence method to study the invariants of this system under diffeomorphisms of the form…

Here we give a complete group classification of the general case of linear systems of three second-order ordinary differential equations excluding the case of systems which are studied in the literature. This is given as the initial step in…

We show that every 2nd order ODE defines a 4-parameter family of projective connections on its 2-dimensional solution space. In a special case of ODEs, for which a certain point transformation invariant vanishes, we find that this family of…

We express the first jet bundle of curves in Euclidean space as homogeneous spaces associated to a Galilean-type group. Certain Cartan connections on a manifold with values in the Lie algebra of the Galilean group are characterized as…

We unearth the interconnection between various analytical methods which are widely used in the current literature to identify integrable nonlinear dynamical systems described by third-order nonlinear ordinary differentiable equations…

Conformal geodesics are solutions to a system of third order of equations, which makes a Lagrangian formulation problematic. We show how enlarging the class of allowed variations leads to a variational formulation for this system with a…

A characterization of the symmetry algebra of the $n$th order ordinary differential equations (ODEs) with maximal symmetry and all third order linearizable ODEs is given. This is used to show that such an algebra $\mathfrak{g}$ determines…