Related papers: Notes on Lie symmetry group methods for differenti…
Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this method together the generalized fundamental theorem of double reduction. In particular, Noether symmetries and some associated…
A review is given of some recently obtained results on analytic contractions of Lie algebras and Lie groups and their applications to special function theory.
We present spectral methods developed in our group to solve three-dimensional partial differential equations. The emphasis is put on equations arising from astrophysical problems in the framework of general relativity.
In many applications, one encounters signals that lie on manifolds rather than a Euclidean space. In particular, covariance matrices are examples of ubiquitous mathematical objects that have a non Euclidean structure. The application of…
I will sketchily illustrate how the theory of symmetry helps in determining solutions of (deterministic) differential equations, both ODEs and PDEs, staying within the classical theory. I will then present a quick discussion of some more…
symmetry, group classification, differential invariants, Lie-classical method,infinitesimal criterion method, RDC equation, KPP equation, similarity solutions.
These notes aim to provide a classical approach to solving some conformable differential equations based on prior knowledge of how to solve ordinary differential equations. That is, using the methods of separation of variables, homogeneous…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants.…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
We use the geometric approach to the theory of Lie systems of differential equations in order to study dissipative Ermakov systems. We prove that there is a superposition rule for solutions of such equations. This fact enables us to express…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in…
We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been…
Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to study different examples and use…
This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…
The generalized symmetry method is applied to a class of completely discrete equations including the Adler-Bobenko-Suris list. Assuming the existence of a generalized symmetry, we derive a few integrability conditions suitable for testing…
The notion of the characteristic Lie algebra of the discrete hyperbolic type equation is introduced. An effective algorithm to compute the algebra for the equation given is suggested. Examples and further applications are discussed.
These lecture notes for a graduate course present an introduction to the mathematical theory of finite element methods for the numerical solution of partial differential equations. Covered are conforming and nonconforming (in particular,…