Related papers: Lie Group analysis of Plasma equilibrium equations
An open question in the field of non-equilibrium statistical physics is whether there exists a unique way through which non-equilibrium systems equilibrate irrespective of how far they are away from equilibrium. To answer this question we…
This work represents a PhD thesis concerning three main topics. The first one deals with the study and applications of Lie systems with compatible geometric structures, e.g. symplectic, Poisson, Dirac, Jacobi, among others. Many new Lie…
An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary…
Admissible point transformations of classes of $r$th order linear ordinary differential equations (in particular, the whole class of such equations and its subclasses of equations in the rational form, the Laguerre-Forsyth form, the first…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The…
After a short review of the classical Lie theorem, a finite dimensional Lie algebra of vector fields is considered and the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a…
We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
This paper describes the classification of analytic $q$-difference equations. The difference Galois groups are computed. A tentative description of the universal difference Galois group is given.
The interaction of partially ionized plasmas with an electromagnetic field is investigated using quantum statistical methods. A general statistical expression for the current density of a plasma in an electromagnetic field is presented and…
This paper is dedicated to the differential Galois theory in the complex analytic context for Lie-Vessiot systems. Those are the natural generaliza- tion of linear systems, and the more general class of differential equations adimitting…
We use group theoretic methods to obtain the extended Lie point symmetries of the equations of motion for a charged particle in the field of a monopole. Cases with certain model magnetic fields and potentials are also studied. Our analysis…
We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total…
In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry…
We investigated the analytical solution of fractional order K(m,n) type equation with variable coefficient which is an extended type of KdV equations into a genuinely nonlinear dispersion regime. By using the Lie symmetry analysis, we…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
We introduce the notion of Gamma-Lie bialgebra, where Gamma is a group. These objects give rise to cocommutative co-Poisson algebras, for which we construct quantization functors. This enlarges the class of co-Poisson algebras for which a…
We derive self-consistent formalism for the description of multi-component partially ionized solar plasma, by means of the coupled equations for the charged and neutral components for an arbitrary number of chemical species, and the…