scholarly journals Exp-Function Method with Computer Symbolic Computation for Exact Solutions of A Nonlinear Differential Equation

2015 ◽  
Author(s):  
Sheng Zhang ◽  
Dong-Dong Liu
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Nonlinear Differential Equation ◽  
Symbolic Computation ◽  
Function Method

scholarly journals Exact Solutions of the Vakhnenko-Parkes Equation with Complex Method

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Yongyi Gu ◽  
Wenjun Yuan ◽  
Najva Aminakbari ◽  
Qinghua Jiang
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Nonlinear Differential Equation ◽  
Computer Simulations ◽  
Complex Method

We derive exact solutions to the Vakhnenko-Parkes equation by means of the complex method, and then we illustrate our main results by some computer simulations. We can apply the idea of this study to related nonlinear differential equation.

A Study on Rational Solutions to a KP-like Equation

2015 ◽  
Vol 70 (4) ◽  
pp. 263-268 ◽  
Author(s):  
Yufeng Zhang ◽  
Wen-Xiu Ma
Keyword(s):  
Differential Equation ◽  
Prime Number ◽  
Nonlinear Differential Equation ◽  
Symbolic Computation ◽  
Bilinear Form ◽  
Differential Operators ◽  
Rational Solutions ◽  
Polynomial Solutions ◽  
Bilinear Equation

AbstractA KP-like nonlinear differential equation is introduced through a generalised bilinear equation which possesses the same bilinear form as the standard KP bilinear equation. By symbolic computation, nine classes of rational solutions to the resulting KP-like equation are generated from a search for polynomial solutions to the corresponding generalised bilinear equation. Three generalised bilinear differential operators adopted are associated with the prime number p=3.

Two New Applications of the Modified Extended Tanh-Function Method

2003 ◽  
Vol 58 (1) ◽  
pp. 39-44 ◽  
Author(s):  
S. A. Elwakil ◽  
S. K. El-labany ◽  
M. A. Zahran ◽  
R. Sabry
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Function Method ◽  
New Exact Solutions ◽  
New Applications

Based on a modified extended tanh-function method and symbolic computation, new exact solutions are found for a soliton breaking equation and coupled kdv system. The obtained solutions include rational, soliton, singular and periodical solutions.

scholarly journals A Nonlinear Differential Equation Related to the Jacobi Elliptic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Kim Johannessen
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Nonlinear Differential Equation ◽  
Elliptic Function ◽  
Polar Angle ◽  
Elliptic Functions ◽  
Jacobi Elliptic Function ◽  
Jacobi Elliptic Functions ◽  
Poisson Equations ◽  
Poisson Boltzmann

A nonlinear differential equation for the polar angle of a point of an ellipse is derived. The solution of this differential equation can be expressed in terms of the Jacobi elliptic function dn(u,k). If the polar angle is extended to the complex plane, the Jacobi imaginary transformation properties and the dependence on the real and complex quarter periods can be described. From the differential equation of the polar angle, exact solutions of the Poisson Boltzmann and the sinh-Poisson equations are found in terms of the Jacobi elliptic functions.

Data Processing in Abound Solutions of (2 + 1)-dimensional Boussinesq Equation

2014 ◽  
Vol 1056 ◽  
pp. 215-220
Author(s):  
Han Kun Gong ◽  
Xiao Shan Zhao ◽  
Guan Hua Zhao
Keyword(s):  
Data Processing ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Function Method ◽  
Boussinesq Equation ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Solitary Solutions

In this paper, the repeated exp-function method is applied to construct exact traveling wave solutions of the (2+1)-dimensional Boussinesq equation. With aid of symbolic computation, many generalized solitary solutions, periodic solutions and other exact solutions are successfully obtained. Thus, it is proved that the method is straightforward and effective to solve the nonlinear evolutions equations.

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.

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