Related papers: Lie Group analysis of Plasma equilibrium equations
A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining…
These are lecture notes of a course on symmetry group analysis of differential equations, based mainly on P. J. Olver's book 'Applications of Lie Groups to Differential Equations'. The course starts out with an introduction to the theory of…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and nonlinear) PDEs, where the term ``weak solution'' comprises the following settings: (a) Distributional solutions. (b) Solutions in…
The $k$-symplectic structures appear in the geometric study of the partial differential equations of classical field theories. Meanwhile, we present a new application of the $k$-symplectic structures to investigate a type of systems of…
In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used.…
The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the…
Using the basic prolongation method and the infinitesimal criterion of invariance, we find the most general Lie point symmetries group of the Thomas equation. Looking the adjoint representation of the obtained symmetry group on its Lie…
We perform a detailed classification of the Lie point symmetries and of the resulting similarity transformations for the Generalized Boiti-Leon-Pempinelli equations. The latter equations for a system of two nonlinear 1+2 partial…
Lie symmetry group method is applied to study the Telegraph equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…
In this book, I explored differential equations for operation in Lie group and for representations of group Lie in a vector space.
We describe kinetic simulations of transient problems in partially ionized weakly-collisional plasma around spherical bodies absorbing or emitting charged particles. Numerical solutions of kinetic equations for electrons and ions in 1D2V…
It is proposed to use the Lie group theory of symmetries of differential equations to investigate the system of equations describing a static star in a radiative and convective equilibrium. It is shown that the action of an admissible group…
It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the B\"acklund transformations. Several new examples of such transformations are found. In particular we obtained the B\"acklund…
This paper presents the continuous and discrete variational formulations of simple thermodynamical systems whose configuration space is a (finite dimensional) Lie group. We follow the variational approach to nonequilibrium thermodynamics…
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
In this contribution, a mathematical framework is constructed to relate and compare non-linear partial differential equations (PDEs) in the category of smooth manifolds. In particular, it can be used to compare those aspects of field…
Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite-difference equations approximating ordinary differential equations.…
The fully nonlinear governing equations for spin 1/2 quantum plasmas are presented. Starting from the Pauli equation, the relevant plasma equations are derived, and it is shown that nontrivial quantum spin couplings arise, enabling studies…