29 citations · 174 across the 54 of their papers we have counts for
32 papers · 1 filter
Classification of real Lie algebras of dimension four
Mehdi Nadjafikhah
We present an exhaustive, coordinate-free, and self-contained classification of four-dimensional real Lie algebras up to isomorphism. In dimension three, classification schemes fre…
Classification of real Lie algebras of dimension one, two and three
Mehdi Nadjafikhah
We present an exhaustive, self-contained, and coordinate-free structural classification of real Lie algebras of dimensions one, two, and three up to isomorphism. In dimensions one…
Cartan equivalence method on fifth-order differential operator
Morteza Bakhshandeh, Rohollah Bakhshandeh-Chamazkoti, Mehdi Nadjafikhah
In this paper, we carry out the equivalence problem for fifth-order differential operators on the line under general fiber-preserving transformation using the Cartan method of equi…
On the invariance properties of Vaidya-Bonner geodesics via symmetry operators
Davood Farrokhi, Rohollah Bakhshandeh-Chamazkoti, Mehdi Nadjafikhah
In the present paper, we try to investigate the Noether symmetries and Lie point symmetries of the Vaidya-Bonner geodesics. Classification of one-dimensional subalgebras of Lie poi…
Preliminary Group Classification and some exact solutions of 2Hessian equation
Mahdieh Yourdkhany, Mehdi Nadjafikhah, Megerdich Toomanian
We study the class of 3-dimensional nonlinear 2-hessian equations mentioned in the text. We perform preliminary group classification on 2-hessian equation. In fact, we find additio…
Contact equivalence problem for KDV-type equations
Mostafa Hesamiarshad, Mehdi Nadjafikhah
The Cartan's method of equivalence and moving coframe method has been applied to solve the local equivalence problem for KDV-type equations under the action of a pseudo-group of co…
Computation of Partially Invariant Solutions for the Einstein Walker Manifolds' Identifying Equations
Mehdi Nadjafikhah, Mehdi Jafari
In this paper, partially invariant solutions (PISs) method is applied in order to obtain new four-dimensional Einstein Walker manifolds. This method is based on subgroup classifica…
Symmetry Reduction of the Two-Dimensional Ricci Flow Equation
Mehdi Nadjafikhah, Mehdi Jafari
This paper is devoted to obtain the one-dimensional group invariant solutions of the two-dimensional Ricci flow ((2D) Rf) equation. By classifying the orbits of the adjoint represe…
The equivariant moving frame method of third order differential equations
Mehdi Nadjafikhah, Rohollah Bakhshandeh Chamazkoti
This paper is devoted to apply the equivariant moving frame method to study the local equivalence problem of third order ordinarily differential equation under the pseudo-group of…
Some general new Einstein Walker manifolds
Mehdi Nadjafikhah, Mehdi Jafari
In this paper, Lie symmetry group method is applied to find the lie point symmetries group of a PDE system that is determined general form of four-dimensional Einstein Walker manif…
G-set Theory and Applications in Lie Theory
Reza Aghayan, Mehdi Nadjafikhah
This paper is devoted to the development and applications of some (new) basic concepts in Lie theory, both from `computational" and "observability" viewpoint. We specify set of all…
Potential symmetries and conservation laws for generalized quasilinear hyperbolic equations
M. Nadjafikhah, R. Bakhshandeh Chamazkoti, F. Ahangari
Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit fo…
Cartan equivalence problem for third order differential operators
Mehdi Nadjafikhah, Rohollah Bakhshandeh-Chamazkoti
This article is dedicated to solve the equivalence problem for two third order differential operators on the line under general fiber--preserving transformation using the Cartan me…
Group Analysis of Born-Infeld Equation
Mehdi Nadjafikhah, Seyed Reza Hejazi
Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetr…
Web geometry of a system of n first order autonomous ordinary differential equations
Mehdi Nadjafikhah
Let , () be a system of first order autonomous ordinary differential equations. We use E. Cartan's equivalence method to study the in…
Symmetry Group of Surfaces PDE
Mehdi Nadjafikhah, Parastoo Kabinejad
Using the theory of the symmetry group for PDEs [15, 17], we derive the symmetry group G associated to surfaces PDE. Several group invariant solutions of the surfaces PDE are given…
Preliminarily group classification of a class of 2D nonlinear heat equations
Mehdi Nadjafikhah, Rouholah Bakhshandeh Chamazkoti
A preliminary group classification of the class 2D nonlinear heat equations , where is arbitrary smooth function of the variables $x,y,u,u_…
Symmetry group classification for general Burger's equation
Mehdi Nadjafikhah, Rouholah Bakhshandeh-Chamazkoti
The present paper solves the problem of the group classification of the general Burgers' equation , where and are arbitrary smooth functions o…
Geometry of Distributions and Gordon equation
Mehdi Nadjafikhah, Reza Aghayan
In this paper we describe the geometry of distributions by their symmetries, and present a simplified proof of the Frobenius theorem and some related corollaries. Then, we study th…
Exact solution of generalized inviscid Burgers' equation
Mehdi Nadjafikhah
Let be integrable functions, nowhere zero, and be invertible. An exact solution to the generalized nonhomogeneous inviscid Burgers…
Group analysis of three dimensional Euler equations of gas dynamics
Mehdi Nadjafikhah
In this paper, the equations governing the unsteady flow of a perfect polytropic gas in three space dimensions are considered. The basic similarity reductions for this system are p…
Fuzzy Lie Groups
M. Nadjafikhah, R. Bakhshandeh-Chamazkoti
In this paper, we have tried to apply the concepts of fuzzy sets to Lie groups and its relative concepts. First, we define a fuzzy submanifold after reviewing ${\cal C…
A symmetry classification for a class of (2+1)-nonlinear wave equation
Mehdi Nadjafikhah, Rohollah Bakhshandeh-Chamazkoti, Ali Mahdipour-Shirayeh
In this paper, a symmetry classification of a -nonlinear wave equation where is a smooth function on , using Lie group method, is gi…
Symmetry Analysis for a New Form of the Vortex Mode Equation
Mehdi Nadjafikhah, Ali Mahdipour--Shirayeh
Giving a new form of the vortex mode equation by a proper change of parameter, our aim is to analyze the point and contact symmetries of the new equation. Fundamental invariants an…