A Riccati–Bernoulli sub-ODE Method for Some Nonlinear Evolution Equations

Author:

Hassan S. Z.1,Abdelrahman Mahmoud A. E.23

Affiliation:

1. Department of Mathematics, College of Science and Humanities - Imam Abdulrahman Bin Faisal University, Al-Jubail12020, Saudi Arabia

2. Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

3. Department of Mathematics, Faculty of Science, Mansoura University, 35516Mansoura, Egypt

Abstract

AbstractThis article concerns with the construction of the analytical traveling wave solutions for the model of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave and the higher-order nonlinear Schrödinger equation by Riccati–Bernoulli sub-ODE method. We give the exact solutions for these two equations. The proposed method is effective tool to solve many other nonlinear partial differential equations. Moreover, this method can give a new infinite sequence of solutions. These solutions are expressed by hyperbolic, trigonometric and rational functions. Finally, with the aid of Matlab release 15, some graphical simulations were designed to see the behavior of these solutions.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

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