Related papers: Lie families: theory and applications
We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of planar Hamiltonian…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector…
By using Lie symmetry methods, we identify a class of second order nonlinear ordinary differential equations invariant under at least one dimensional subgroup of the symmetry group of the Ermakov-Pinney equation. In this context, nonlinear…
We perform enhanced Lie symmetry analysis of generalized fifth-order Korteweg-de Vries equations with time-dependent coefficients. The corresponding similarity reductions are classified and some exact solutions are constructed.
As fragments of first-order logic, Description logics (DLs) do not provide nonmonotonic features such as defeasible inheritance and default rules. Since many applications would benefit from the availability of such features, several…
Superderivations for the eight families of finite or infinite dimensional graded Lie superalgebras of Cartan-type over a field of characteristic $p>3$ are completely determined by a uniform approach: The infinite dimensional case is reduced…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
The existence of a formal particular solution (family of solutions) of oscillating type under certain conditions has been proved for the quasi-linear ordinary differential equations system. The asymptotic nature of this solution (the family…
We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…
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 give explicit criteria of solvability for families of linear systems on time scales. We introduce a new method of embedding a time scale into a non-autonomous system of ODEs. This will be the first step to implementing the structural…
Fundamentals on Lie group methods and applications to differential equations are surveyed. Many examples are included to elucidate their extensive applicability for analytically solving both ordinary and partial differential equations.
In this article, a general family of bivariate distributions is used to model competing risks data with dependent factors. The general structure of competing risks data considered here includes ties. A comprehensive inferential framework…
We start discussing basic properties of Lie groupoids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and the subsequent integration of partial differential equations which is the…
Using the adjoint representations of Lie algebras, we classify all Jacobi structures on real two- and three-dimensional Lie groups. Also, we study Jacobi-Lie systems on these real low-dimensional Lie groups. Our results are illustrated…
We formulate and prove a twofold generalisation of Lie's second theorem that integrates homomorphisms between formal group laws to homomorphisms between Lie groups. Firstly we generalise classical Lie theory by replacing groups with…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…