scholarly journals RETRACTED: <i>The Modified Simple Equation Method and Its Applications in Mathematical Physics and Biology</i>

2015 ◽  
Vol 05 (01) ◽  
pp. 1-17
Author(s):  
Mahmoud A. E. Abdelrahman ◽  
Magdi Hakeem Armanious ◽  
Emad H. M. Zahran ◽  
Mostafa M. A. Khater
Keyword(s):  
Mathematical Physics ◽  
Simple Equation ◽  
Equation Method ◽  
Modified Simple Equation Method

scholarly journals Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1986
Author(s):  
Noha M. Rasheed ◽  
Mohammed O. Al-Amr ◽  
Emad A. Az-Zo’bi ◽  
Mohammad A. Tashtoush ◽  
Lanre Akinyemi
Keyword(s):  
Short Pulse ◽  
Soliton Solutions ◽  
Kerr Nonlinearity ◽  
Mathematical Physics ◽  
Higher Order ◽  
Simple Equation ◽  
Equation Method ◽  
Computational Work ◽  
The Difference ◽  
Modified Simple Equation Method

This paper studies the propagation of the short pulse optics model governed by the higher-order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity. Exact one-soliton solutions are derived for a generalized case of the NLSE with the aid of software symbolic computations. The modified Kudryashov simple equation method (MSEM) is employed for this purpose under some parametric constraints. The computational work shows the difference, effectiveness, reliability, and power of the considered scheme. This method can treat several complex higher-order NLSEs that arise in mathematical physics. Graphical illustrations of some obtained solitons are presented.

Optical soliton perturbation with Gerdjikov–Ivanov equation by modified simple equation method

Optik ◽  
2018 ◽  
Vol 157 ◽  
pp. 1235-1240 ◽  
Author(s):  
Anjan Biswas ◽  
Yakup Yildirim ◽  
Emrullah Yasar ◽  
Houria Triki ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Optical Soliton ◽  
Simple Equation ◽  
Equation Method ◽  
Soliton Perturbation ◽  
Modified Simple Equation Method

scholarly journals New Soliton Solutions of the (2+1)-Dimensional System Davey-Stewartson Equation

2018 ◽  
Vol 7 (4.1) ◽  
pp. 37 ◽  
Author(s):  
Anwar J Ja'afar Mohamad Jawad ◽  
Mahmood J. Abu-Al Shaeer ◽  
Marko D. Petkovi_c
Keyword(s):  
Soliton Solutions ◽  
Travelling Wave ◽  
Simple Equation ◽  
Equation Method ◽  
Initial System ◽  
Wave Transformation ◽  
Dimensional System ◽  
Modified Simple Equation Method ◽  
Complex Coefficients

In this paper, we derive several soliton solutions of the generalized Davey-Stewartson equation with the complex coefficients. First we use the travelling wave transformation to reduce the initial system to ODE. The equivalent ODE is then solved, giving several classes of solutions, depending on the values of the parameters. Finally, the Extended Tanh-Coth method and Modified simple equation method.  

scholarly journals The Modified Simple Equation Method for Exact and Solitary Wave Solutions of Nonlinear Evolution Equation: The GZK-BBM Equation and Right-Handed Noncommutative Burgers Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Kamruzzaman Khan ◽  
M. Ali Akbar ◽  
Norhashidah Hj. Mohd. Ali
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Simple Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Modified Simple Equation Method ◽  
Bbm Equation

The modified simple equation method is significant for finding the exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. In this paper, we bring in the modified simple equation (MSE) method for solving NLEEs via the Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony (GZK-BBM) equation and the right-handed noncommutative Burgers' (nc-Burgers) equations and achieve the exact solutions involving parameters. When the parameters are taken as special values, the solitary wave solutions are originated from the traveling wave solutions. It is established that the MSE method offers a further influential mathematical tool for constructing the exact solutions of NLEEs in mathematical physics.

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