In the framework of projective-geometric theory of systems of differential equations developed by the authors, this paper studies the group properties of systems of two (resolved with respect to the second derivatives) second-order ordinary differential equations whose right-hand sides are polynomials of the third degree with respect to the derivatives of the unknown functions. A classification of such systems admitting four-dimensional symmetry group of the Lie-Petrov type VI 1 is given. For each of the systems, a necessary and sufficient linearization criterion is obtained, i.e., the authors find the necessary and sufficient conditions under which, by a change of variables, the system can be reduced to a differential system whose integral...
We discuss the Lie symmetry approach to homogeneous, linear, ordinary differential equations in an a...
Abstract. Complex Lie point transformations are used to linearize a class of systems of second order...
In order to apply Lie's symmetry theory for solving a differential equation it must be possible to i...
In the framework of projective-geometric theory of systems of differential equations developed by th...
In the framework of the projective geometric theory of systems of differential equations, which is b...
It is proved that every projective connection on an n-dimensional manifold M is locally defined by a...
The methods of differential geometry, in particular, the methods of Cartan's theory of projecti...
The solution of a class of third order ordinary differential equations possessing two parameter Lie ...
Transformations of differential equations to other equivalent equations play a central role in many ...
AbstractThere are seven equivalence classes of second-order ordinary differential equations possessi...
We present here, in compact form, the necessary and sufficient conditions for linearization of third...
Linearizability criteria for systems of two cubically semi-linear second order ordinary differential...
The linearization problem for scalar third-order ordinary differential equations via point transform...
Cartan's method of equivalence is used to prove that there exists two fundamental tensorial invarian...
The subject of this article are third-order differential equations that may be linearized by a varia...
We discuss the Lie symmetry approach to homogeneous, linear, ordinary differential equations in an a...
Abstract. Complex Lie point transformations are used to linearize a class of systems of second order...
In order to apply Lie's symmetry theory for solving a differential equation it must be possible to i...
In the framework of projective-geometric theory of systems of differential equations developed by th...
In the framework of the projective geometric theory of systems of differential equations, which is b...
It is proved that every projective connection on an n-dimensional manifold M is locally defined by a...
The methods of differential geometry, in particular, the methods of Cartan's theory of projecti...
The solution of a class of third order ordinary differential equations possessing two parameter Lie ...
Transformations of differential equations to other equivalent equations play a central role in many ...
AbstractThere are seven equivalence classes of second-order ordinary differential equations possessi...
We present here, in compact form, the necessary and sufficient conditions for linearization of third...
Linearizability criteria for systems of two cubically semi-linear second order ordinary differential...
The linearization problem for scalar third-order ordinary differential equations via point transform...
Cartan's method of equivalence is used to prove that there exists two fundamental tensorial invarian...
The subject of this article are third-order differential equations that may be linearized by a varia...
We discuss the Lie symmetry approach to homogeneous, linear, ordinary differential equations in an a...
Abstract. Complex Lie point transformations are used to linearize a class of systems of second order...
In order to apply Lie's symmetry theory for solving a differential equation it must be possible to i...