scholarly journals Exp-function method for a nonlinear ordinary differential equation and new exact solutions of the dispersive long wave equations

2009 ◽  
Vol 58 (11-12) ◽  
pp. 2294-2299 ◽  
Author(s):  
Sheng Zhang ◽  
Jing-Lin Tong ◽  
Wei Wang
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Exact Solutions ◽  
Function Method ◽  
Wave Equations ◽  
Nonlinear Ordinary Differential Equation ◽  
New Exact Solutions ◽  
Long Wave

The Exp-function Method for the Riccati Equation and Exact Solutions of Dispersive Long Wave Equations

2008 ◽  
Vol 63 (10-11) ◽  
pp. 663-670 ◽  
Author(s):  
Sheng Zhang ◽  
Wei Wang ◽  
Jing-Lin Tong
Keyword(s):  
Exact Solutions ◽  
Riccati Equation ◽  
Function Method ◽  
Wave Equations ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Mathematical Tool ◽  
New Exact Solutions ◽  
Long Wave

In this paper, the Exp-function method is used to seek new generalized solitonary solutions of the Riccati equation. Based on the Riccati equation and one of its generalized solitonary solutions, new exact solutions with three arbitrary functions of the (2+1)-dimensional dispersive long wave equations are obtained. Compared with the tanh-function method and its extensions, the proposed method is more powerful. It is shown that the Exp-function method provides a straightforward and important mathematical tool for solving nonlinear evolution equations in mathematical physics.

scholarly journals On finite series solutions of conformable time-fractional Cahn-Allen equation

2020 ◽  
Vol 9 (1) ◽  
pp. 194-200 ◽  
Author(s):  
Asim Zafar ◽  
Hadi Rezazadeh ◽  
Khalid K. Ali
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Exact Solutions ◽  
Fractional Order ◽  
Symbolic Computation ◽  
Nonlinear Ordinary Differential Equation ◽  
Hyperbolic Function ◽  
Series Solutions ◽  
Finite Series ◽  
New Exact Solutions

AbstractThe aim of this article is to derive new exact solutions of conformable time-fractional Cahn-Allen equation. We have achieved this aim by hyperbolic function and expa function methods with the aid of symbolic computation using Mathematica. This idea seems to be very easy to employ with reliable results. The time fractional Cahn-Allen equation is reduced to respective nonlinear ordinary differential equation of fractional order. Also, we have depicted graphically the constructed solutions.

New Exact Solutions to (2+1)-Dimensional Dispersive Long Wave Equations

2004 ◽  
Vol 42 (6) ◽  
pp. 811-813 ◽  
Author(s):  
Zhi Hong-Yan ◽  
Lü Zhuo-Sheng ◽  
Zhang Hong-Qing
Keyword(s):  
Exact Solutions ◽  
Wave Equations ◽  
New Exact Solutions ◽  
Long Wave

Regarding Rational Exponential and Hyperbolic Functions Solutions of Conformable Time-Fractional Phi-four Equation

2018 ◽  
Author(s):  
Asim Zafar ◽  
Alper Korkmaz ◽  
Bushra Khalid ◽  
Hadi Rezazadeh
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Function Method ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Hyperbolic Function Method ◽  
Projected Methods

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

On the Exact Solutions of the Thomas Equation by Algebraic Methods

2015 ◽  
Vol 16 (2) ◽  
pp. 73-77 ◽  
Author(s):  
K. S. Al-Ghafri
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Algebraic Methods ◽  
Wave Transformation ◽  
Transformation Technique ◽  
Main Form ◽  
New Exact Solutions ◽  
Thomas Equation

AbstractThe Thomas equation is studied to obtain new exact solutions. The wave transformation technique is applied to simplify the main form of the Thomas equation from partial differential equation (PDE) to an ordinary differential equation (ODE). The modified tanh and ($$G'/G$$)-expansion methods are used with the aid of Maple software to arrive at exact solutions for the Thomas equation. Many types of solutions are obtained.

scholarly journals New exact solutions of coupled generalized regularized long wave equations

2017 ◽  
Vol 25 (4) ◽  
pp. 400-405 ◽  
Author(s):  
K.R. Raslan ◽  
Talaat S. EL-Danaf ◽  
Khalid K. Ali
Keyword(s):  
Exact Solutions ◽  
Wave Equations ◽  
New Exact Solutions ◽  
Long Wave

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.

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