Application of Extended Transformed Rational Function Method to Some (3+1) Dimensional Nonlinear Evolution Equations

2018 ◽  
pp. 433-437
Keyword(s):  
Rational Function ◽  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Mapping Method ◽  
Nonlinear Evolution Equations ◽  
Petviashvili Equation ◽  
Complexiton Solutions ◽  
Transformed Rational Function Method

The transformed rational function method can be considered as unification of the tanh type methods, the homogeneous balance method, the mapping method, the exp-function method and the F-expansion type methods. In this paper, we present complexiton solutions of (3+1) dimensional Korteweg-de Vries (KdV) equation and a new (3+1) dimensional generalized Kadomtsev-Petviashvili equation by using extended transformed rational function method which provides very useful and effective way to obtain complexiton solutions of nonlinear evolution equations.

Extended Transformed Rational Function Method to Nonlinear Evolution Equations

2019 ◽  
Vol 20 (6) ◽  
pp. 691-701 ◽  
Author(s):  
Emrullah Yaşar ◽  
Yakup Yıldırım ◽  
Abdullahi Rashid Adem
Keyword(s):  
Rational Function ◽  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Trigonometric Function ◽  
Nonlinear Evolution Equations ◽  
Bilinear Forms ◽  
Complexiton Solutions ◽  
Transformed Rational Function Method ◽  
Hirota Bilinear

AbstractIn this work, we study complexiton solutions to a (2+1)-dimensional (SK) equation and a (3+1)-dimensional nonlinear evolution equation. The complexiton solutions are combinations of trigonometric function waves and exponential function waves. For this goal, the extended transformed rational function method is carried out which is based on the Hirota bilinear forms of the considered equations and provides a systematical and convenient tool for constructing the exact solutions of nonlinear evolution equations.

scholarly journals Some Methods about Finding the Exact Solutions of Nonlinear Modified BBM Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Fan Niu ◽  
Jianming Qi ◽  
Zhiyong Zhou
Keyword(s):  
Exact Solutions ◽  
Rational Function ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Complex Method ◽  
First Time ◽  
Bbm Equation

Finding exact solutions of nonlinear equations plays an important role in nonlinear science, especially in engineering and mathematical physics. In this paper, we employed the complex method to get eight exact solutions of the modified BBM equation for the first time, including two elliptic function solutions, two simply periodic solutions, and four rational function solutions. We used the exp − ϕ z -expansion methods to get fourteen forms of solutions of the modified BBM equation. We also used the sine-cosine method to obtain eight styles’ exact solutions of the modified BBM equation. Only the complex method can obtain elliptic function solutions. We believe that the complex method presented in this paper can be more effectively applied to seek solutions of other nonlinear evolution equations.

Exact Soliton Solutions of the Variable Coefficient KdV Equation with Forced Term

2014 ◽  
Vol 548-549 ◽  
pp. 1196-1200
Author(s):  
Yong Mei Bao ◽  
Siqintana Bao
Keyword(s):  
Variable Coefficient ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Nonlinear Ordinary Differential Equation ◽  
Variable Coefficients ◽  
Nonlinear Evolution Equations ◽  
Forced Term ◽  
Exact Soliton Solutions

In order to construct exact soliton solutions of nonlinear evolution equations with variable coefficients. By using a transformation, the variable coefficient KdV equation with forced Term is reduced to nonlinear ordinary differential equation (NLODE), after that, a number of exact solitons solutions of variable coefficient KdV equation with forced Term are obtained by using the equation shorted in NLODE. As it showed above, this kind of method can be applied in solving a large number of nonlinear evolution equations.

Application of the Exp-Functionmethod to the Riccati Equation and New Exact Solutions with Three Arbitrary Functions of Quantum Zakharov Equations

2008 ◽  
Vol 63 (10-11) ◽  
pp. 646-652 ◽  
Author(s):  
Mohamed A Abdou ◽  
Essam M. Abulwafa
Keyword(s):  
Exact Solutions ◽  
Riccati Equation ◽  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Mathematical Tool ◽  
New Exact Solutions ◽  
Generalized Riccati Equation ◽  
Solitary Solutions

The Exp-function method with the aid of the symbolic computational system is used for constructing generalized solitary solutions of the generalized Riccati equation. Based on the Riccati equation and its generalized solitary solutions, new exact solutions with three arbitrary functions of quantum Zakharov equations are obtained. It is shown that the Exp-function method provides a straightforward and important mathematical tool for nonlinear evolution equations in mathematical physics.

scholarly journals Further Results about Traveling Wave Exact Solutions of the (2+1)-Dimensional Modified KdV Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yang Yang ◽  
Jian-ming Qi ◽  
Xue-hua Tang ◽  
Yong-yi Gu
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Mkdv Equation ◽  
Nonlinear Evolution Equations ◽  
Complex Method ◽  
Modified Kdv Equation

We used the complex method and the exp(-ϕ(z))-expansion method to find exact solutions of the (2+1)-dimensional mKdV equation. Through the maple software, we acquire some exact solutions. We have faith in that this method exhibited in this paper can be used to solve some nonlinear evolution equations in mathematical physics. Finally, we show some simulated pictures plotted by the maple software to illustrate our results.

AN EFFICIENT METHOD FOR FINDING THE EXACT SOLUTION OF NONLINEAR EVOLUTION EQUATIONS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1703-1706 ◽  
Author(s):  
XIQIANG ZHAO ◽  
DENGBIN TANG ◽  
CHANG SHU
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

In this paper, based on the idea of the homogeneous balance method, the special truncated expansion method is improved. The Burgers-KdV equation is discussed and its many exact solutions are obtained with the computerized symbolic computation system Mathematica. Our method can be applied to finding exact solutions for other nonlinear partial differential equations too.

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