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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Angheluta-Bauer, Luiza / Chen, Xi / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi / Yang, Xu


IMPACT FACTOR 2018: 1.033
5-year IMPACT FACTOR: 1.106

CiteScore 2018: 1.11

SCImago Journal Rank (SJR) 2018: 0.288
Source Normalized Impact per Paper (SNIP) 2018: 0.510

Mathematical Citation Quotient (MCQ) 2017: 0.12

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2191-0294
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Volume 20, Issue 3-4

Issues

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

S. Z. Hassan
  • Department of Mathematics, College of Science and Humanities - Imam Abdulrahman Bin Faisal University, Al-Jubail 12020, Saudi Arabia
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/ Mahmoud A. E. Abdelrahman
  • Corresponding author
  • Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
  • Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
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  • Other articles by this author:
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Published Online: 2019-04-02 | DOI: https://doi.org/10.1515/ijnsns-2018-0045

Abstract

This 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.

Keywords: Riccati–Bernoulli sub-ODE method; ion sound wave; Langmuir wave; Schrödinger equation; traveling wave solutions; Matlab release 15

MSC 2010: 35A20; 35A99; 83C15; 65Z05

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About the article

Received: 2018-02-24

Accepted: 2019-01-12

Published Online: 2019-04-02

Published in Print: 2019-05-26


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 20, Issue 3-4, Pages 303–313, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2018-0045.

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