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Solitary Wave Solutions of Some Nonlinear Physical Models Using Riccati Equation Approach

Acta Mathematicae Applicatae Sinica 2020年第2期36卷 401-418页

作者： zaid odibat Ahmed ALSAEDI Tasawar HAYAT School of Basic Sciences and umanities German Jordanian UniversityAmman 11180Jordan Nonlinear Analysis and Applied Mathematics(NAAM)Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics Quaid-I-Azam UniversityIslamabad 44000Pakistan

Riccati equation approach is used to look for exact travelling wave solutions of some nonlinear physical *** wave solutions are established for the modified KdV equation,the Boussinesq equation and the Zakharov-Kuznetsov *** generalized solitary wave solutions with some free parameters are *** obtained solutions,which includes some previously known solitary wave solutions and some new ones,are expressed by a composition of Riccati differential equation solutions followed by a *** employed approach,which is straightforward and concise,is expected to be further employed in obtaining new solitary wave solutions for nonlinear physical problems.

关键词： solitary wave solution Riccati equation the modified KdV equation the Boussinesq equation the Zakharov-Kuznetsov equation

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The Multi-Step Differential Transform Method and Its Application to Determine the Solutions of Non-Linear Oscillators

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Advances in Applied Mathematics and Mechanics 2012年第4期4卷 422-438页

作者： Vedat Suat Erturk zaid M.odibat Shaher Momani Department of Mathematics Faculty of Arts and SciencesOndokuz Mayis University55139SamsunTurkey Prince Abdullah Bin Ghazi Faculty of Science and IT Al-Balqa Applied UniversityAl-Salt 19117Jordan The University of Jordan Faculty of ScienceDepartment of MathermaticsAmman 1194Jordan

In this paper,a reliable algorithm based on an adaptation of the standard differential transform method is presented,which is the multi-step differential transform method(MSDTM).The solutions of non-linear oscillators were obtained by *** comparisons between the MSDTM and the classical fourthorder Runge-Kutta method(RK4)reveal that the proposed technique is a promising tool to solve non-linear oscillators.

关键词： Non-linear oscillatory systems differential transform method numerical solution

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Differential Transform Method and Numerical Simulation of Chaotic Ecological Models

Differential Transform Method and Numerical Simulation of Ch...

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第三世界生态高峰会

作者： zaid odibat Cyrille Bertelle M.A.Aziz-Alaoui Prince Abdullah Bin Ghazi Faculty of Science and IT Al-Balqa'Applied University Salt.Jordan LITIS University of Le Havre 25 rue Ph.Lebon.BP 540 76058 Le Havre cedex.France LMAH University of Le Havre 25 rue Ph.Lebon BP 540 76058 Le Havre cedex France

This paper is concerned with the implementation of the Differential Transform Method (DTM) for getting solutions of complex or chaotic dynamical systems,like ecological mathematical *** first present this DTM analytical *** systems are well knowned to be hard according to the aceuraeity of the numerical approximation methods like Runge-Kutta 4 (RK4).Then we apply,for such systems, the DTM and we compare the result of nnmerical solutions obtained with RK4 numerical approximation *** attention is paid to ecological,two-or three-,species models,where complex or chaotic properties can be detected.

关键词： Differential Transform Method and Numerical Simulation of Chaotic Ecological Models

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Numerical Approach for Interaction Systems Solving using Differential Transform Method-Simulation of Lotka-Volterra System and Epidemic Model

Numerical Approach for Interaction Systems Solving using Dif...

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第三世界生态高峰会

作者： zaid odibat Cyrille Bertelle Gérard H.E Duchamp Prince Abdullah Bin Ghazi Faculty of Science and IT Al-Balqa'Apphed University Salt Jordan LITIS.University of Le Havre 25 rue Ph.Lebon BP 540 76058 Le Havre cedex France LIPN-UMR CNRS 7030 University of Paris 13.99 rue J.-B.Clément 93430 Villetaneuse France

In this article,we propose a formal definition of analytical representation of interaction *** give a general scheme tosolve them using Differential Transform *** Lotka-Volterra System and epidemic model can be considered as examples of these analytical representations of interaction *** differential transform method is employed to solve the system of the nonlinear differential equations governing on these specific *** focus on the generation of the transformed recurrence relations to build a solver for the problems and to make an *** results illustrates the reliability and the performance of the method.

关键词： Volterra Model Numerical Approach for Interaction Systems Solving using Differential Transform Method-Simulation of Lotka-Volterra System and Epidemic Model

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