Bogoyavlenskij symmetries of ideal MHD equilibria as Lie point transformations

Bogoyavlenskij Symmetries of Isotropic and Anisotropic MHD Equilibria as Lie Point Transformations

Isotropic Magnetohydrodynamic (MHD) Equilibrium Equations and generalized Anisotropic Magnetohydrodynamic (Chew–Goldberger–Low, CGL) Equilibrium Equations possess infinite-dimensional groups of intrinsic symmetries. We show that certain non-trivial Lie point transformations (that can be obtained by direct application of the general Lie group analysis method) are equivalent to Bogoyavlenskij sym...

A Diffusion Equation with Exponential Nonlinearity Recant Developments

The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...

New Solutions for Fokker-Plank Equation of‎ ‎Special Stochastic Process via Lie Point Symmetries

‎In this paper Lie symmetry analysis is applied in order to find new solutions for Fokker Plank equation of Ornstein-Uhlenbeck process‎. ‎This analysis classifies the solutions format of the Fokker Plank equation by using the Lie algebra of the symmetries of our considered stochastic process‎.

Exact MHD solutions with crystallographic symmetries and non-interacting Fourier modes

Polynomial and non-polynomial solutions set for wave equation with using Lie point symmetries

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...