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).

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.

scholarly journals Perturbation-Iteration Method for First-Order Differential Equations and Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mehmet Şenol ◽  
İhsan Timuçin Dolapçı ◽  
Yiğit Aksoy ◽  
Mehmet Pakdemirli
Keyword(s):  
Differential Equation ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Single Equation ◽  
Iteration Algorithm ◽  
First Order ◽  
New Perturbation ◽  
First Time ◽  
Good Agreement

The previously developed new perturbation-iteration algorithm has been applied to differential equation systems for the first time. The iteration algorithm for systems is developed first. The algorithm is tested for a single equation, coupled two equations, and coupled three equations. Solutions are compared with those of variational iteration method and numerical solutions, and a good agreement is found. The method can be applied to differential equation systems with success.

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 Numerical solution of two dimensional time fractional-order biological population model

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 177-186 ◽  
Author(s):  
Amit Prakash ◽  
Manoj Kumar
Keyword(s):  
Approximate Solution ◽  
Fractional Order ◽  
Iteration Method ◽  
Population Model ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Spatial Diffusion ◽  
Two Dimensional ◽  
Degenerate Problem ◽  
Biological Population

AbstractIn this work, we provide an approximate solution of a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model using a fractional variational iteration method (FVIM). Four test illustrations are used to show the proficiency and accuracy of the projected scheme. Comparisons between exact solutions and numerical solutions are presented for different values of fractional orderα.

Sign in / Sign up

Export Citation Format

Share Document