Mehdi Nadjafikhah

• Professor
• Professor (Full) at Iran University of Science and Technology

This paper focuses on investigating the equivalence problem for fifth-order differential operators (FODOs) on the line under general fiber-preserving transformations. Utilizing the Cartan method of equivalence, the study specifically addresses the gauge equivalence problem, seeking to establish the conditions for two FODOs to be related by a fiber-...

The paper examines a numerical show of a human T-cell lymphotropic infection sort I HTLV transmission of CD4+ T-cells. “The model allows for CD4+ T cell subsets of susceptible, latently infected, and actively infected cells and leukemia cells. In fact, this mathematical model in the fractional differential system form describes the interaction betw...

The classical symmetry method is often employed to find precise solutions to differential equations. This method has yielded several new symmetry reductions and exact solutions for numerous theoretically and physically relevant partial differential equations. These results, as well as the symmetries of a variety of specific cases of the Fokker–Plan...

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 equivalence. Two versions of equivalence problems have been solved. We consider the direct equivalence problem and an equivalence problem to determine the sufficient and nece...

The Lie symmetry group of the Zabolotskaya-Khokhlov equation has been seriously studied, earlier than this. Eventually, it has been endowed with a general model by N.J.C. Ndogmo, in 2008. This research is devoted to introducing the algebra, the group, and the reductions of a new symmetry which is an exception of that model.

In this paper, we will calculate an integrating factor, first integral, and reduce the order of the non-Linear second-order ODEs , through the λ-symmetry method. Moreover, we compute an integrating factor, first integral and reduce the order for particular cases of this equation.

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 point symmetries is considered. In fact, the collection of pairwise non-conjugate one-dimensional subalgebras that are called the optimal system of subalgebras is determined...

So far, numerous methods for solving and analyzing differential equations are proposed. Meanwhile; the combined methods are beneficial; one of them is the Optimized MRA method (OMRA). This method is based on the Father wavelets (dependent on the invariant solutions obtained by the Lie symmetry method) and correspondent MRA. In this paper, we apply...

In this paper, by using the Lie symmetry analysis method of fractional differential equations, we construct the geometric vector fields of time-fractional Burger-Fisher equation, and then the symmetry reductions are also presented. In addition, we obtained the conservation laws by Ibrgimov's nonlocal method to time-fractional partial differential e...

In this article, by using the Herman–Pole technique the conservation laws of the (3+1)−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(3+1)-$\end{document} Jimbo–Miwa e...

The three-dimensional Zabolotskaya-Khokhlov equation (ZK) is an important example of sound wave propagation equations. In this paper, the Lie point symmetry group method is applied to find similarity solutions of this equation. The solutions can be used to clarifying the propagation of a bounded two-dimensional acoustic beam in nonlinear medias.

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 point symmetries are considered. In fact, the collection of pairwise non-conjugate one-dimensional subalgebras that are called the optimal system of subalgebras is determine...

In this paper, we show that every homogeneous Finsler metric is a weakly stretch metric if and only if it reduces to a weakly Landsberg metric. This yields an extension of Tayebi–Najafi’s result that proved the result for the class of stretch Finsler metrics. Let F:=αϕ(β/α) be a homogeneous weakly stretch (α,β)-metric on a manifold M. We show that...

This PowerPoint has been prepared for the "General Topology course" based on "J.R. Munkres, Topology, Pearson; 2nd Edition, 2000". which I presented in the first semester of the academic year 2020-2021 at Iran University of Science and Technology.

In this paper, we will concentrate on a systematic investigation of finding Lie point symmetries of the nonlinear [Formula: see text]-dimensional time-fractional Kramers equation via Riemann–Liouville and Caputo derivatives. By using the Lie group analysis method, the invariance properties and the symmetry reductions of the time-fractional Kramers...

This PowerPoint has been prepared for the "General Topology course" based on "J.R. Munkres, Topology, Pearson; 2nd Edition, 2000". which I presented in the first semester of the academic year 2020-2021 at Iran University of Science and Technology.

This PowerPoint has been prepared for the "General Topology course" based on "J.R. Munkres, Topology, Pearson; 2nd Edition, 2000". which I presented in the first semester of the academic year 2020-2021 at Iran University of Science and Technology.

This PowerPoint has been prepared for the "General Topology course" based on "J.R. Munkres, Topology, Pearson; 2nd Edition, 2000". which I presented in the first semester of the academic year 2020-2021 at Iran University of Science and Technology.

This paper systematically investigates the Lie symmetry analysis of a class of 3-dimensional non-linear 2-Hessian equations \(u_{xx}u_{yy}+u_{xx}u_{yy}+u_{yy}u_{zz}=u_{xy}^2+u_{yz}^2+u_{xz}^2+f\), where f is an arbitrary smooth function f of the variables (x, y, z). In fact, the preliminary group classification of the 2-Hessian equation was carried...

Differential algebra (DA) methods are currently being exploited for analyzing dynamic biosystem models for their structural identifiability (SI) properties. An early step in this approach entails finding an equivalent input–output (I/O) model. A recent approach for finding these equations, based on Grbner bases and imbedded in the app COMBOS is rel...

Lie symmetry group method is applied to find the Lie point symmetry group of a system of partial differential equations that determines general form of four-dimensional Einstein Walker manifold. Also we will construct the optimal system of one-dimensional Lie subalgebras and investigate some of its group invariant solutions.

In this article, we applied our method (WTM) on the generalized version of FKPP and obtained the new analytical solutions for non-constant coefficients.

The numerous methods for solving differential equations exist, every method have benefits and drawbacks, in this field, the combined methods are very useful, one of them is the wavelet transform method (WTM). This method based on the wavelets and corresponding wavelet transform, that dependent on the differential invariants obtained by the Lie symm...

In this paper, group analysis of the time-fractional Harmonic Oscillator equation with Riemann–Liouville derivative is performed and its reduced fractional ordinary differential equations are determined. With the aid of the concept of nonlinear self-adjoint and the fractional generalization of the Noether operators are obtained concerved vector for...

This paper systematically investigates the Lie symmetry analysis of the time-fractional Buckmaster equation in the sense of Riemann–Liouville fractional derivative. With the aid of infinitesimal symmetries, this equation is transformed into a nonlinear ordinary differential equation of fractional order (FODE), where the fractional derivatives are i...

This book is the first volume of a two-volume series on Calculus. This book is based on the author's experience in teaching "General Mathematics" at various universities over a period of more than 25 years.

This book is the second volume of a two-volume series on Calculus. This book is based on the author's experience in teaching "General Mathematics" at various universities over a period of more than 25 years.

Some exact solutions of KdV-Burgers-Kuramoto (KBK) equation are derived by the anzas and tanh methods. Also, the most general Lie point symmetry group of the KBK equation are presented using the basic Lie symmetry method. As well as, the non-classical and weak symmetries of this equation, as well as the corresponding similarity reductions, are inve...

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 additional equivalence transformation on the space (x,y,z,u,f), with the aid of a method, then we take their projections on the space (x,y,z,f), so we prove an optimal system of...

In the last decade it has been shown by the present authors and various co-workers, that all of the complete statistical approaches of turbulence based on Naiver-Stokes equations i.e. the infinite set of multi-point moment equations, the infinite hierarchy of multi-point probability-density equations and the Hopf functional equation admit more symm...

Nowadays, wavelets have been widely used in various fields of science and technology. Meanwhile, the wavelet transforms and the generation of new Mother wavelets are noteworthy. In this paper, we generate new Mother wavelets and analyze the differential equations by using of their corresponding wavelet transforms. This method by Mother wavelets and...

Noether's First Theorem guarantees conservation laws provided that the Lagrangian is invariant under a Lie group action. In this paper, via the concept of Killing vector fields and the Minkowski metric, we first construct an important Lie group, known as Hyperbolic Rotation-Translation group. Then, according to Gonçalves and Mansfield's method, we...

دراین مقاله، لینکیج -nمیله ای ، فضای پیکربندی آن و بردار طول عمومی را تعریف می کنیم. با استفاده از قضیۀ مجموعه تراز منظم نشانمی دهیم فضای پیکربندی هر لینکیج - nمیله ای با بردار طول عمومی، منیفلد همواری از بعد n − ٣می باشد. همچنین برای درک بهتر ساختارهندسی لینکیج -nمیله ای، توپولوژی لینکیج -۴میله ای و فضای پیکربندی آن را با جزئیات بیشتر توضیح می ده...

Nowadays, wavelets have been widely used in various fields of science and technology. Meanwhile, the wavelet transforms and the generation of new Mother wavelets are noteworthy. In this paper, we generate new Mother wavelets and analyze the differential equations by using of their corresponding wavelet transforms. This method by Mother wavelets and...

The numerous methods for solving differential equations are exist, every method have benefits and draw backs, in this field, the combined methods are very useful, one of them is the wavelet transform method (WTM). This method based on the wavelets and corresponding wavelet transforms, that dependent on the differential invariants obtained by the Li...

So far, the numerous methods for solving and analyzing differential equations are proposed, meanwhile, the combined methods are very useful, one of them is the Optimized MRA method (OMRA). This method based on the Father wavelets (dependent on the invariant solutions obtained by the Lie symmetry method) and correspondent MRA. In this paper, we appl...

There are many tools for analyzing PDEs. In the equivalence theory, the symmetry methods like the Lie symmetry and Fushchych methods are tools for solving PDEs. Indeed, these methods can determine classical and non-classical invariants and then by reformulating the equations according to these invariants, they can reduce the order of PDEs and conve...

In this paper, we consider the Ricci soliton structure on closed and orientable pseudo-Riemannian manifolds. We construct examples of non-trivial, i.e., non-Einstein steady Lorentzian Ricci solitons on indecomposable closed Lorentzian 3–manifolds admitting a parallel light-like vector field with closed orbits. These non-trivial examples that are no...

The powerful tools for analyzing problems and equations are offered by the wavelet theory in the numerous scientific fields. In this paper, new father wavelets with two independent variables according to the differential invariants are designed and the novel method based on those are proposed, new father wavelets are produced, the multiresolution a...

In harmonic analysis, wavelets are useful and important tools for analyzing problems and equations. As far as we know, the wavelet applications for solving differential equations are limited to solving either ODE or PDE by numerical means. In this paper, the new mother wavelets with two independent variables are designed in accordance with differen...

We obtain a complete group classification of the Lie point symmetries of nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using this result we study their Noether symmetries and establish the respective conservation laws. It is shown that the projection of the Lie point symmetries on M are special subgroups of the conformal g...

The wavelets are important functions in the harmonic analysis. Up to our knowledge, apply wavelets to solve differential equations are limited to ODEs or PDEs with approximate and numerical solutions. In this paper, the novel methods based on the wavelets with two independent variables according to differential invariants are proposed. In fact, the...

The Lie symmetry and Fushchych methods are useful tools for analyzing PDEs‎. ‎By these methods‎, ‎we can determine classical and non-classical invariants and then by reformulating the equations according to these invariants‎, ‎we can reduce the order of PDEs and convert them to ODEs. ‎In this paper‎, ‎we apply the Lie symmetry and Fushchych methods...

In this paper, the Lie approximate symmetry analysis is applied to investigate new exact solutions of the singularly perturbed Boussinesq equation. The tanh-function method, is employed to solve some of the obtained reduced ordinary differential equations.We construct new analytical solutions with small parameter which is effectively obtained by th...

In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find t...

Lie symmetry group theory is one of the most important methods in analysis of differential equations. Such Lie groups are invertible point transformations which result in the movement of dependent and independent variables of the differential equations. Constructing the solutions of nonlinear PDEs, mapping them to another solution by linear transfo...

We present a method for automatically solving apictorial jigsaw puzzles [as shown by Hoff, D., and Olver, P.J., Automatic solution of jigsaw puzzles, J. Math. Imaging Vision 49 (2014) 234-250.] that is based on an extension of the method of differential invariant signature [Hoff, D., and Olver, P.J., Extensions of invariant signatures for object re...

In this paper, we prove that equation 2 ( ) 2 3 = 0 t x t x x x x E ≡ u −u + u f u − au u − buu is self-adjoint and quasi self-adjoint, then we construct conservation laws for this equation using its symmetries. We investigate a symmetry classification of this nonlinear third order partial differential equation, where f is smooth function on u and...

A presentation file for the course "An Introduction to Reimannian Geometry".

A presentation file for the section 01 of course ”An Introduction to Riemannian Geometry”.

A presentation file for the section 02 of course ”An Introduction to Riemannian Geometry”.

A presentation file for the section 03 of course ”An Introduction to Riemannian Geometry”.

A presentation file for the section 00 of course ”An Introduction to Riemannian Geometry”.

A presentation file for the section 06 of course ”An Introduction to Riemannian Geometry”.

A presentation file for the section 04 of course ”An Introduction to Riemannian Geometry”.

A presentation file for the section 05 of course ”An Introduction to Riemannian Geometry”.

The symmetry of the Bagley–Torvik equation is investigated by using the Lie group analysis method. The Bagley–Torvik equation in the sense of the Riemann–Liouville derivatives is considered. Then we prove a Noetherlike theorem for fractional Lagrangian densities with the Riemann-Liouville fractional derivative and few examples are presented as an a...

Fushchych method is a useful method for analysing PDEs, by this method we can determine Non-classical invariants, standard, weak and partial symmetries. These symmetries are called Non-classical symmetries. PDE with these symmetries have exact solutions. In this paper, we apply Fushchych method on generalized version of FKPP equation f(x).u_tt(x, t...

In this article, we reduce the Boiti-Leon-Manna-Pempinelli (BLMP) equation to an ordinary differential equation by the Lie symmetry method. Then, we calculate infinite structural equations from Maurer-Cartan's infinite forms for the symmetrical pseudo-group of this equation, by invariantized defining equation method. Finally using the multiplier me...

In this paper, two methods of approximate symmetries for partial differential equations with a small parameter are applied to a perturbed nonlinear Ostrovsky equation. To compute the first-order approximate symmetry, we have applied two methods which one of them was proposed by Baikov et al. in which the infinitesimal generator is expanded in a per...

The mathematical model of the gravitational waves of the Milne spacetime is a linear second order partial differential equation, known as the Gordon equation, dependent on a functional parameter. In this paper, by applying a symmetry method for this equation, its new Lie reductions are obtained, in the general form of the parameter. Then, its three...

In this attempt, the stability of a connection on Hermitian vector bundles over a Riemannian manifold for the generalized Jensen-type functional equation (Formula presented.) is discussed. In fact, the main purpose of this paper is to prove the generalized Hyers–Ulam–Rassias stability of connection on between Hermitian (Formula presented.) and (For...

The main objective for this thesis is interducing diffeology and diffeological spaces. Also we will consider some diffeological structures like differential forms on diffeological spaces. This thesis lead to an explanation for diffeological way to solve a problem.

The application of Lie group theory for solving differential equations is an important concentrating on topic of Lie groups theory about physical sciences and applied mathematics. This thesis is centralized on the introduction of Lie symmetry groups to reducing, and solving general differential equations, also, considering three examples of them. O...

Dear Honored Professors, Colleagues and Students, I have a great pleasure to extend to you all, a very warm welcome on behalf of the scientific and organizing committees of the 8th Seminar on Geometry and Topology in Amirkabir University of Technology (Tehran Polytechnic) which will be held in Dec. 15-17, preceding by a Workshop on 13-14 Dec. 2015....

The moving coframe method is applied to solve the local equivalence problem for a class of linear fourth-order telegraph equations, in two independent variables under action of a pseudo-group of contact transformations to determine necessary and sufficient conditions for a class of linear fourth-order telegraph equations to be equivalent to simples...

This thesis is devoted to the comprehensive investigation of symmetries and conservation laws of partial differential equations. The current thesis consists of six separate main chapters. In the following, we mention the main topic of each chapter. In chapter one, the classical Lie symmetry method and classification of sub-algebras is presented. C...

Emulate the gating mechanism of ionic channels in neurons, we present a mathematical model for the time constant of dynamical systems. Our model is an analytical continues function. The analyses give evidence that one can adjust the desirable morphology of the response of the dynamical system by adjusting the parameters of the proposed model.

In this thesis, we study �-symmetry method for ordinary differential equations that lacks non-trivial Lie symmetry to reduce the order and find general solution of them. Also, proposed method to find integrating factor and first integral using �-symmetry method for n-order ordinary differential equations. Finally, in order to reduce the order of pa...

The purpose of this thesis is to consider Backlund transformation as an important tool for working with wide range of the nonlinear partial differential equation. This thesis is presented in five chapters. The main reference is [11]. Chapter one gives a small glance at Backlund transformation history such that the reader gets familiar with two main...

In this paper, three similarity solutions of a mathematical model for the gravitational waves of the Milne expanding empty spacetime, namely, the Gordon-type equation of the Milne metric will be determined. This equation is a linear second-order partial differential equation, dependent on a functional parameter. Formerly, some Lie reductions of the...

In the present paper, conservation laws of the tri-Hamiltonain system of equations Whitham-Broer-Kaup (WBK) are investigated by applying the first homotopy formula. Hamiltonian symmetries of the system are constructed by using the corresponding Hamiltonian operators and the conserved densities.

Lecture ”An Introduction to Manifolds - Begining”

Lecture ”An Introduction to Manifolds - 01 - Smooth Functions on a Euclidean Space”

Lecture ”An Introduction to Manifolds - 02 - Tangent Vectors in R^n as Derivations”

Lecture ”An Introduction to Manifolds - 09 - Sub-manifolds”

Lecture ”An Introduction to Manifolds - 12 - The Tangent Bundle”

Lecture ”An Introduction to Manifolds - 13 - Bump Functions and Partitions of Unity”

Lecture ”An Introduction to Manifolds - 16 - Lie Algebras”

Lecture ”An Introduction to Manifolds - 04 - Differential Forms on R^n”

Lecture ”An Introduction to Manifolds - 05 - Manifolds”

Lecture ”An Introduction to Manifolds - 06 - Smooth Maps on a Manifold”

Lecture ”An Introduction to Manifolds - 10 - Categories and Functors”

Lecture ”An Introduction to Manifolds - 03 - Alternating k-Linear Functions”

Lecture ”An Introduction to Manifolds - 07 - Quotients”

Lecture ”An Introduction to Manifolds - 08 - The Tangent Space”

Lecture ”An Introduction to Manifolds - 17 - Differential 1-Forms”