scholarly journals Analytical Wave Solutions for Foam and KdV-Burgers Equations Using Extended Homogeneous Balance Method

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 729 ◽  
Author(s):  
U.M. Abdelsalam ◽  
M. G. M. Ghazal
Keyword(s):  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Industrial Applications ◽  
Nonlinear Evolution Equations ◽  
Balance Method ◽  
Wave Solutions ◽  
Engineering Sciences ◽  
Foam Drainage Equation ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

In this paper, extended homogeneous balance method is presented with the aid of computer algebraic system Mathematica for deriving new exact traveling wave solutions for the foam drainage equation and the Kowerteg-de Vries–Burgers equation which have many applications in industrial applications and plasma physics. The method is effective to construct a series of analytical solutions including many types like periodical, rational, singular, shock, and soliton wave solutions for a wide class of nonlinear evolution equations in mathematical physics and engineering sciences.

scholarly journals Travelling Wave Solutions for Fisher’s Equation Using the Extended Homogeneous Balance Method

2021 ◽  
Vol 26 (1) ◽  
pp. 22-30
Author(s):  
Mohammad M. Fares ◽  
Usama M. Abdelsalam ◽  
Faiza M. Allehiany
Keyword(s):  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Balance Method ◽  
Fisher Equation ◽  
Travelling Wave Solutions ◽  
Fisher’S Equation ◽  
Wave Solutions ◽  
Fisher's Equation ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

In this work, the extended homogeneous balance method is used to derive exact solutions of nonlinear evolution equations. With the aid of symbolic computation, many new exact travelling wave solutions have been obtained for Fisher’s equation and Burgers-Fisher equation. Fisher’s equation has been widely used in studying the population for various systems, especially in biology, while Burgers-Fisher equation has many physical applications such as in gas dynamics and fluid mechanics. The method used can be applied to obtain multiple travelling wave solutions for nonlinear partial differential equations.

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 New Solutions of Elastic Waves in an Elastic Rod under Finite Deformation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Peng Guo ◽  
Xiang Wu ◽  
Liangbi Wang
Keyword(s):  
Elliptic Function ◽  
Finite Deformation ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Mapping Method ◽  
Nonlinear Evolution Equations ◽  
Elastic Rod ◽  
Weierstrass Elliptic Function ◽  
Wave Solutions ◽  
Trigonometric Function Solutions

The nonlinear wave equation of an elastic rod under finite deformation is solved by the extended mapping method. Abundant new exact traveling wave solutions for this equation are obtained, which contain trigonometric function solutions, solitary wave solutions, Jacobian elliptic function solutions, and Weierstrass elliptic function solutions. The method can be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in 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
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