scholarly journals Travelling wave solutions for a generalized Fisher equation

1982 ◽  
Vol 85 (2) ◽  
pp. 287-290 ◽  
Author(s):  
Mostafa A Abdelkader
Keyword(s):  
Travelling Wave ◽  
Fisher Equation ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Generalized Fisher Equation

scholarly journals Some New Non-Travelling Wave Solutions of the Fisher Equation with Nonlinear Auxiliary Equation

2018 ◽  
Vol 3 (2) ◽  
pp. 92-101
Author(s):  
Anika Tashin Khan ◽  
Hasibun Naher
Keyword(s):  
Evolution Equations ◽  
Expansion Method ◽  
Travelling Wave ◽  
Nonlinear Ordinary Differential Equation ◽  
Nonlinear Evolution Equations ◽  
Fisher Equation ◽  
Auxiliary Equation ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Functional Forms

We have generated many new non-travelling wave solutions by executing the new extended generalized and improved (G'/G)-Expansion Method. Here the nonlinear ordinary differential equation with many new and real parameters has been used as an auxiliary equation. We have investigated the Fisher equation to show the advantages and effectiveness of this method. The obtained non-travelling solutions are expressed through the hyperbolic functions, trigonometric functions and rational functional forms. Results showing that the method is concise, direct and highly effective to study nonlinear evolution equations those are in mathematical physics and engineering.

MULTIPLE SOLITON SOLUTIONS FOR THE NAGUMO EQUATION AND THE MODIFIED GENERAL BURGERS-FISHER EQUATION

2006 ◽  
Vol 03 (03) ◽  
pp. 371-381 ◽  
Author(s):  
H. A. ABDUSALAM
Keyword(s):  
Time Delay ◽  
Function Method ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Fisher Equation ◽  
Travelling Wave Solutions ◽  
Limit Case ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Nagumo Equation

A generalized tanh-function method is used for constructing exact travelling wave solutions for Nagumo's equation and the modified generalized Burger-Fisher equation. Also new multiple soliton solutions are obtained for both equations. Limit case of the time delay is studied and the results of the general Burgers-Fisher equations are verified.

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.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

scholarly journals Singularity analysis and analytic solutions for the Benney–Gjevik equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
P. G. L. Leach
Keyword(s):  
Evolution Equations ◽  
Singularity Analysis ◽  
Analytic Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Painlevé Test ◽  
Wave Solutions ◽  
Algebraic Solutions

Abstract We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

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