A variety of exact solutions of the (2+1)-dimensional modified Zakharov–Kuznetsov equation

2021 ◽  
Author(s):  
Emad H. M. Zahran ◽  
Ahmet Bekir ◽  
Hijaz Ahmed
Keyword(s):  
Plasma Physics ◽  
Exact Solutions ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Point Of View ◽  
Simple Equation ◽  
Equation Method ◽  
Good Comparison ◽  
Approach Method

From the point of view of two distinct methods, we will construct new multiple types of private exact solutions of the (2+1)-dimensional modified Zakharov–Kuznetsov equation (MZKE) which is a famous model in plasma physics. The suggested methods for this purpose are the extended simple equation method (ESEM) and the Paul–Painleve approach method (PPAM). Moreover, the numerical solutions corresponding to the achieved solutions are demonstrated in the framework of the variational iteration method (VIM). Furthermore, we will demonstrate a good comparison not only between our achieved solutions but also with that realized previously by other authors who studied this model before.

Painlevé approach and its applications to get new exact solutions of three biological models instead of its numerical solutions

2020 ◽  
Vol 34 (29) ◽  
pp. 2050270
Author(s):  
Ahmet Bekir ◽  
Emad H. M. Zahran
Keyword(s):  
Nonlinear Dynamics ◽  
Exact Solutions ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Chain Model ◽  
Biological Models ◽  
Double Chain ◽  
New Model ◽  
New Exact Solutions

This paper focuses on realizing the exact solutions of three distinct important biological models using the Painlevé approach. These three models are the nonlinear dynamics of microtubules — a new model, the Kundu–Eckhaus model and the double chain model of DNA. Furthermore, the numerical solutions of these three equations have been achieved using the variational iteration method.

scholarly journals Variational Iteration Method for Volterra Functional Integrodifferential Equations with Vanishing Linear Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Konuralp ◽  
H. Hilmi Sorkun
Keyword(s):  
Exact Solutions ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Integrodifferential Equations ◽  
Test Problems ◽  
Application Process ◽  
Delay Function ◽  
Variational Iteration

Application process of variational iteration method is presented in order to solve the Volterra functional integrodifferential equations which have multi terms and vanishing delays where the delay functionθ(t)vanishes inside the integral limits such thatθ(t)=qtfor0<q<1,t≥0. Either the approximate solutions that are converging to the exact solutions or the exact solutions of three test problems are obtained by using this presented process. The numerical solutions and the absolute errors are shown in figures and tables.

scholarly journals New Lump Solutions for Spatio-Temporal Dispersion (1+1)-Dimensional Ito-Equation

2021 ◽  
Author(s):  
Maha Shehata ◽  
Emad Zahran ◽  
Ahmet Bekir
Keyword(s):  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Point Of View ◽  
Lump Solutions ◽  
Personal Profile ◽  
Ode Method ◽  
Approach Method ◽  
Spatio Temporal ◽  
Ito Equation ◽  
Temporal Dispersion

From point of view of two different schemas several new impressive lump solutions to (1+1)-dimensional Ito equation have been established. The first schema is the Paul-Painleve approach method (PPAM) which will be applied perfectly to extract multiple lump solutions of this model, while the second schema is the famous one of the ansatze method and has personal profile named the Ricatti-Bernolli Sub-ODE method. In related subject the numerical solutions corresponding to all lump solutions achieved via each method have been demonstrated individually in the framework of the variational iteration method (VIM).

Soliton solutions of the (3 + 1)-dimensional Yu–Toda–Sassa–Fukuyama equation by the new approach and its numerical solutions

2020 ◽  
pp. 2150025
Author(s):  
Ahmet Bekir ◽  
Emad H. M. Zahran ◽  
Özkan Güner
Keyword(s):  
Fluid Dynamics ◽  
Plasma Physics ◽  
Nonlinear Wave ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Soliton Solutions ◽  
Variational Iteration Method ◽  
Dispersive Media ◽  
New Approach ◽  
First Time

In this paper, we will solve the (3 + 1)-dimensional Yu–Toda–Sassa–Fukuyama equation (YTSFE) which widely investigates the dynamics of solitons and nonlinear wave arising in a fluid dynamics, plasma physics and weakly dispersive media. The Paul-Painlevé approach (PPA) is used for the first time to achieve the soliton solutions of this equation. Furthermore, the numerical solutions of this equation have been proposed by using the variational iteration method (VIM).

scholarly journals An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
A. Barari ◽  
M. Omidvar ◽  
D. D. Ganji ◽  
Abbas Tahmasebi Poor
Keyword(s):  
Fluid Mechanics ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Iteration Method ◽  
Structural Engineering ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Nonlinear Boundary Value Problems ◽  
Linear And Nonlinear

Variational iteration method (VIM) is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM). The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems.

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