scholarly journals Traveling Wave Solutions of Nonlinear Evolution Equations Via the Modified Simple Equation Method

2017 ◽  
Vol 3 (2) ◽  
pp. 20 ◽  
Author(s):  
A. K. M. Kazi Sazzad Hossain
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Simple Equation ◽  
Equation Method ◽  
Wave Solutions ◽  
Modified Simple Equation Method

scholarly journals Traveling-Wave Solution of Modified Liouville Equation by Means of Modified Simple Equation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-4 ◽  
Author(s):  
Md. Abdus Salam
Keyword(s):  
Liouville Equation ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Nonlinear Evolution Equations ◽  
Simple Equation ◽  
Equation Method ◽  
New Approach ◽  
Modified Simple Equation Method

We construct the traveling wave solutions involving parameters of modified Liouville equation by using a new approach, namely the modified simple equation method. The proposed method is direct, concise, and elementary and can be used for many other nonlinear evolution equations.

scholarly journals New exact traveling wave solutions for DS-I and DS-II equations

2012 ◽  
Vol 17 (3) ◽  
pp. 369-378 ◽  
Author(s):  
Ahmet Yildirim ◽  
Ameneh Samiei Paghaleh ◽  
Mohammad Mirzazadeh ◽  
Hossein Moosaei ◽  
Anjan Biswas
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Solution Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Equation Method ◽  
Wave Solutions ◽  
Simplest Equation Method

In this present work, the simplest equation method is used to construct exact solutions of the DS-I and DS-II equations. The simplest equation method is a powerful solution method for obtaining exact solutions of nonlinear evolution equations. This method can be applied to nonintegrable equations as well as to integrable ones.

Explicit, periodic and dispersive soliton solutions to the conformable time-fractional Wu–Zhang system

2021 ◽  
pp. 2150417
Author(s):  
Kalim U. Tariq ◽  
Mostafa M. A. Khater ◽  
Muhammad Younis
Keyword(s):  
Fractional Derivative ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Conformable Fractional Derivative ◽  
Physical Behavior ◽  
Wave Solutions

In this paper, some new traveling wave solutions to the conformable time-fractional Wu–Zhang system are constructed with the help of the extended Fan sub-equation method. The conformable fractional derivative is employed to transform the fractional form of the system into ordinary differential system with an integer order. Some distinct types of figures are sketched to illustrate the physical behavior of the obtained solutions. The power and effective of the used method is shown and its ability for applying different forms of nonlinear evolution equations is also verified.

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.

scholarly journals Traveling wave solutions of some nonlinear evolution equations

2015 ◽  
Vol 54 (2) ◽  
pp. 263-269 ◽  
Author(s):  
Rafiqul Islam ◽  
Kamruzzaman Khan ◽  
M. Ali Akbar ◽  
Md. Ekramul Islam ◽  
Md. Tanjir Ahmed
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions

CONSTRUCTING FAMILIES TRAVELING WAVE SOLUTIONS IN TERMS OF SPECIAL FUNCTION FOR THE ASYMMETRIC NIZHNIK–NOVIKOV–VESSELOV EQUATION

2004 ◽  
Vol 15 (04) ◽  
pp. 595-606 ◽  
Author(s):  
YONG CHEN ◽  
QI WANG
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Special Function ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Algebraic Method ◽  
Nonlinear Evolution Equations ◽  
Symbolic System ◽  
Wave Solutions

By means of a more general ansatz and the computerized symbolic system Maple, a generalized algebraic method to uniformly construct solutions in terms of special function of nonlinear evolution equations (NLEEs) is presented. We not only successfully recover the previously-known traveling wave solutions found by Fan's method, but also obtain some general traveling wave solutions in terms of the special function for the asymmetric Nizhnik–Novikov–Vesselov equation.

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