Related papers: The Geometry of Fourth Order Differential Operator
This article is dedicated to solve the equivalence problem for two third order differential operators on the line under general fiber--preserving transformation using the Cartan method of equivalence. We will do three versions of the…
In this paper, we carry out the equivalence problem for fifth-order differential operators on the line under general fiber-preserving transformation using the Cartan method of equivalence. Two versions of equivalence problems have been…
We use E. Cartan's method to solve the problem of equivalence of the second order ordinary differential equations with respect to the pseudogroup of point transformations.
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
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…
We apply the Cartan equivalence method to the study of real analytic second order ODEs under the local real analytic diffeomorphism of $\C^2$ which are area-preserving. This enables us to give a characterization of the second order ODEs…
The problem of equivalency for linear differential operators of the first order is discussed.
The linearization problem by use of the Cartan equivalence method for scalar third-order ODEs via point transformations was solved partially in [1,2]. In order to solve this problem completely, the Cartan equivalence method is applied to…
We address the problem of local geometry of third order ODEs modulo contact, point and fibre-preserving transformations of variables. Several new and already known geometries are described in a uniform manner by the Cartan method of…
In this paper, we consider an equivalence problem of second order partially differential equations (PDE) and a duality of the flat differential equation. For the equivalence problem, explicit form of invariants (curvatures) are given. We…
We consider the local equivalence problem for the class of linear second order hyperbolic equations in two independent variables under an action of the pseudo-group of contact transformations. E. Cartan's method is used for finding the…
A PhD thesis written under supervision of Pawel Nurowski and defended at the Faculty of Physics of the University of Warsaw. We adress the problems of local equivalence and geometry of third order ODEs modulo contact, point and…
We apply Cartan's method of equivalence to find a contact integrable extension for the structure equations of the symmetry pseudo-group of the four-dimensional Martinez Alonso - Shabat equation. From the extension we derive two differential…
The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally accosiated with differential…
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…
Bagderina \cite{Bagderina2008} solved the equivalence problem for scalar third-order ordinary differential equations (ODEs), quadratic in the second-order derivative, via point transformations. However, the question is open for the general…
Using Cartan equivalence method, invariant coframes are constructed for two branches of rank one and zero, which characterize linearizable third-order ODEs under contact transformations with four- and five-dimensional Lie symmetry algebras,…
The Cartan's method of equivalence and moving coframe method has been applied to solve the local equivalence problem for KDV-type equations under the action of a pseudo-group of contact transformations. The structure equations, the sets of…
This paper is devoted to apply the equivariant moving frame method to study the local equivalence problem of third order ordinarily differential equation under the pseudo-group of fiber preserving transformations.
We discuss the local and global problems for the equivalence of geometric structures of an arbitrary order and, in later sections, attention is given to what really matters, namely the equivalence with respect to transformations belonging…