scholarly journals Exact solutions of the Biswas-Milovic equation, the ZK(m,n,k) equation and the K(m,n) equation using the generalized Kudryashov method

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 129-139 ◽  
Author(s):  
EL Sayed M.E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Partial Differential Equations ◽  
Exact Solutions ◽  
Power Law ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Pdes ◽  
Hyperbolic Function ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Hyperbolic Function Solutions ◽  
Fibonacci Function

AbstractIn this article, we apply the generalized Kudryashov method for finding exact solutions of three nonlinear partial differential equations (PDEs), namely: the Biswas-Milovic equation with dual-power law nonlinearity; the Zakharov--Kuznetsov equation (ZK(m,n,k)); and the K(m,n) equation with the generalized evolution term. As a result, many analytical exact solutions are obtained including symmetrical Fibonacci function solutions, and hyperbolic function solutions. Physical explanations for certain solutions of the three nonlinear PDEs are obtained.

scholarly journals Generalized Kudryashov Method for Time-Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Yusuf Pandir ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Third Order ◽  
Hilliard Equation ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Cahn Hilliard Equation

In this study, the generalized Kudryashov method (GKM) is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. These time-fractional equations can be turned into another nonlinear ordinary differantial equation by travelling wave transformation. Then, GKM has been implemented to attain exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. Also, some new hyperbolic function solutions have been obtained by using this method. It can be said that this method is a generalized form of the classical Kudryashov method.

scholarly journals New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yusuf Pandir ◽  
Halime Ulusoy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Wave Equations ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Partial Differential ◽  
New Exact Solutions

We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE), we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

scholarly journals The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

2020 ◽  
Vol 66 (6 Nov-Dec) ◽  
pp. 771
Author(s):  
Yusuf Gurefe
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

In this article, we consider the exact solutions of the Hunter-Saxton and Schrödinger equations defined by Atangana's comformable derivative using the general Kudryashov method. Firstly, Atangana's comformable fractional derivative and its properties are included. Then, by introducing the generalized Kudryashov method, exact solutions of nonlinear fractional partial differential equations (FPDEs), which can be expressed with the comformable derivative of Atangana, are classified. Looking at the results obtained, it is understood that the generalized Kudryashov method can yield important results in obtaining the exact solutions of FPDEs containing beta-derivatives.

scholarly journals Applications of an Extended -Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
E. M. E. Zayed ◽  
Shorog Al-Joudi
Keyword(s):  
Exact Solutions ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Expansion Method ◽  
Nonlinear Pdes ◽  
Hyperbolic Function ◽  
Soliton Equation ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Hyperbolic Function Solutions

We construct the traveling wave solutions of the (1+1)-dimensional modified Benjamin-Bona-Mahony equation, the (2+1)-dimensional typical breaking soliton equation, the (1+1)-dimensional classical Boussinesq equations, and the (2+1)-dimensional Broer-Kaup-Kuperschmidt equations by using an extended -expansion method, whereGsatisfies the second-order linear ordinary differential equation. By using this method, new exact solutions involving parameters, expressed by three types of functions which are hyperbolic, trigonometric and rational function solutions, are obtained. When the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions.

Modified Auxiliary Differential Equation Method and Exact Solutions Generalized Schrödinger

2014 ◽  
Vol 513-517 ◽  
pp. 4470-4473 ◽  
Author(s):  
Lin Tian ◽  
Yu Ping Qin
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Equation Method ◽  
Hyperbolic Function ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Solution ◽  
Auxiliary Differential Equation Method ◽  
Differential Equation Method

This paper describes a method on which modify auxiliary differential equation method by using this method for solving nonlinear partial differential equations and with aid of Maple Software ,we get the exact solution of the generalized schrödinger, including hyperbolic function solutions, trigonometric solution.

scholarly journals New extended generalized Kudryashov method for solving three nonlinear partial differential equations

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Reham M.A. Shohib ◽  
Mohamed E.M. Alngar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Nonlinear Partial Differential Equations ◽  
Magnetized Plasma ◽  
Ion Acoustic Waves ◽  
Partial Differential ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
First Time

New extended generalized Kudryashov method is proposed in this paper for the first time. Many solitons and other solutions of three nonlinear partial differential equations (PDEs), namely, the (1+1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity, the (2+1)-dimensional Davey–Sterwatson (DS) equation and the (3+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation of ion-acoustic waves in a magnetized plasma have been presented. Comparing our new results with the well-known results are given. Our results in this article emphasize that the used method gives a vast applicability for handling other nonlinear partial differential equations in mathematical physics.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

New Exact Solutions for Two Nonlinear Equations

2006 ◽  
Vol 61 (1-2) ◽  
pp. 1-6 ◽  
Author(s):  
Zonghang Yang
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Exact Solutions ◽  
Water Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
New Exact Solutions ◽  
Complex Phenomena ◽  
Sivashinsky Equation

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutions for the second were just N-soliton solutions. In this paper we present kinds of new exact solutions by using the extended tanh-function method.

Sign in / Sign up

Export Citation Format

Share Document