Related papers: Lie symmetries of multidimensional difference equa…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
We give a brief introduction to Hamiltonian optics and Lie algebraic methods. We use these methods to describe the operators governing light propagation, refraction and reflection in phase space. The method offers a systematic way to find…
We analyze the classical equations of motion for a particle moving in the presence of a static magnetic field applied in the $ z $ direction, which varies as $ {1\over{x^2}} $. We find the symmetries through Lie's method of group analysis.…
We consider two problems arising in the study of the Schr\"odinger-Newton equations. The first is to find their Lie point symmetries. The second, as an application of the first, is to investigate an approximate solution corresponding to…
It is shown how to define difference equations on particular lattices $\{x_n\}$, $n\in\mathbb{Z}$, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special…
We outline a new, systematic way of constructing and analysing field theories, where all possible continuous symmetries of a given model are derived using the method of Lie point symmetries. If the model has free parameters, and…
In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be…
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
Applying Lie symmetry method, we find the most general Lie point symmetries group of the radiation natural convection flow equation(RNC). Looking the adjoint representation of the obtained symmetry group on its Lie algebra, we will find the…
We derive the Lie and the Noether conditions for the equations of motion of a dynamical system in a $n-$dimensional Riemannian space. We solve these conditions in the sense that we express the symmetry generating vectors in terms of the…
In in this paper we show how using D.A. it is found a simple change of variables (c.v.) that brings us to obtain differential equations simpler than the original one. In a pedagogical way (at least we try to do that) and in order to make…
We show that the recent results of \ [Int. J. Mod. Phys. D 25 (2016) 1650051] on the application of Lie/Noether symmetries in scalar field cosmology are well-known in the literature while the problem could have been solved easily under a…
In this paper, we further consider the symmetry-based method for seeking nonlocally related systems for partial differential equations. In particular, we show that the symmetry-based method for partial differential equations is the natural…
In [Solving second order ordinary differential equations by extending the Prelle-Singer method, J. Phys. A: Math.Gen., 34, 3015-3024 (2001)] we defined a function (we called S) associated to a rational second order ordinary differential…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…