Exact solutions of the Burgers-Huxley equation

2004 ◽  
Vol 68 (3) ◽  
pp. 413-420 ◽  
Author(s):  
O.Yu. Yefimova ◽  
N.A. Kudryashov
Keyword(s):  
Exact Solutions ◽  
Huxley Equation

Exact solutions of the Rosenau–Hyman equation, coupled KdV system and Burgers–Huxley equation using modified transformed rational function method

2018 ◽  
Vol 32 (24) ◽  
pp. 1850282 ◽  
Author(s):  
Yong-Li Sun ◽  
Wen-Xiu Ma ◽  
Jian-Ping Yu ◽  
Chaudry Masood Khalique
Keyword(s):  
Exact Solutions ◽  
Rational Function ◽  
Function Method ◽  
Bernoulli Equation ◽  
Huxley Equation ◽  
Transformed Rational Function Method ◽  
The Given

In this research, we study the exact solutions of the Rosenau–Hyman equation, the coupled KdV system and the Burgers–Huxley equation using modified transformed rational function method. In this paper, the simplest equation is the Bernoulli equation. We are not only obtain the exact solutions of the aforementioned equations and system but also give some geometric descriptions of obtained solutions. All can be illustrated vividly by the given graphs.

scholarly journals A New Numerical Scheme for the Generalized Huxley Equation

2016 ◽  
Vol 16 ◽  
pp. 105-111
Author(s):  
Bilge Inan
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Exact Solutions ◽  
Difference Method ◽  
Present Method ◽  
Numerical Scheme ◽  
Numerical Solutions ◽  
Alternative Method ◽  
Huxley Equation

In this paper, an implicit exponential finite difference method is applied to compute the numerical solutions of the nonlinear generalized Huxley equation. The numerical solutions obtained by the present method are compared with the exact solutions and obtained by other methods to show the efficiency of the method. The comparisons showed that proposed scheme is reliable, precise and convenient alternative method for solution of the generalized Huxley equation.

Exact solutions of the Burgers–Huxley equation via dynamics

2020 ◽  
Vol 151 ◽  
pp. 103615 ◽  
Author(s):  
Alexei G. Kushner ◽  
Ruslan I. Matviichuk
Keyword(s):  
Exact Solutions ◽  
Huxley Equation

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

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