The (G'/G,1/G)-Expansion Method for Solving the (2+1)-Dimensional Breaking Soliton Equations

2013 ◽  
Vol 787 ◽  
pp. 1006-1010
Author(s):  
Yun Jie Yang ◽  
Yun Mei Zhao ◽  
Yan He
Keyword(s):  
Rational Functions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Soliton Equations ◽  
Wave Solutions

In this paper, the-expansion method is applied to construct more general exact travelling solutions of the (2+1)-dimensional breaking soliton equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions.

The G′/G-Expansion Method for Solutions of Evolution Equations

2014 ◽  
Vol 940 ◽  
pp. 425-428
Author(s):  
Chun Huan Xiang ◽  
Bo Liang ◽  
Hong Lei Wang
Keyword(s):  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Nonlinear Problems ◽  
Rational Functions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Wave Solutions

The investigation about traveling wave solutions of nonlinear equations is an important and interesting subject because they play important role in understanding the nonlinear problems. By using the (G′/G)-expansion method proposed recently, we construct the travelling wave solutions involving parameters for the Hirota and Satsuma equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The numerical simulation figures are shown.

scholarly journals Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

2018 ◽  
Vol 6 (06) ◽  
Author(s):  
Figen Kangalgil
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

The investigation of the exact solutions of NLPDEs plays an im- portant role for the understanding of most nonlinear physical phenomena. Also, the exact solutions of this equations aid the numerical solvers to assess the correctness of their results. In this paper, (G'/G)-expansion method is pre- sented to construct exact solutions of the Perturbed Wadati-Segur-Ablowitz equation. Obtained the exact solutions are expressed by the hyperbolic, the trigonometric and the rational functions. All calculations have been made with the aid of Maple program. It is shown that the proposed algorithm is elemen- tary, e¤ective and has been used for many PDEs in mathematical physics.  

scholarly journals The Extended MultipleG′/G-Expansion Method and Its Application to the Caudrey-Dodd-Gibbon Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huizhang Yang ◽  
Wei Li ◽  
Biyu Yang
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Hyperbolic Function ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Special Values ◽  
Wave Solutions ◽  
Complexiton Solutions ◽  
Hyperbolic Function Solutions

An extended multipleG′/G-expansion method is used to seek the exact solutions of Caudrey-Dodd-Gibbon equation. As a result, plentiful new complexiton solutions consisting of hyperbolic functions, trigonometric functions, rational functions, and their mixture with arbitrary parameters are effectively obtained. When some parameters are properly chosen as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solutions.

scholarly journals Exact Solutions of Equation Generated by the Jaulent-Miodek Hierarchy by(G’/G)-Expansion Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Wafaa M. Taha ◽  
M. S. M. Noorani
Keyword(s):  
Exact Solutions ◽  
Traveling Wave Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Solitary Wave Solutions ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Wave Solutions ◽  
Tanh Method ◽  
Dimensional Equation

The(G’/G)-expansion method is proposed for constructing more general exact solutions of the nonlinear(2+1)-dimensional equation generated by the Jaulent-Miodek Hierarchy. As a result, when the parameters are taken at special values, some new traveling wave solutions are obtained which include solitary wave solutions which are based from the hyperbolic functions, trigonometric functions, and rational functions. We find in this work that the(G’/G)-expansion method give some new results which are easier and faster to compute by the help of a symbolic computation system. The results obtained were compared with tanh method.

scholarly journals A Generalized and Improved(G′/G)-Expansion Method for Nonlinear Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
M. Ali Akbar ◽  
Norhashidah Hj. Mohd. Ali ◽  
E. M. E. Zayed
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Rational Functions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Travelling Wave Solutions ◽  
Wave Solutions

A generalized and improved(G′/G)-expansion method is proposed for finding more general type and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty and advantage of the proposed method, we solve the KdV equation, the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation and the strain wave equation in microstructured solids. Abundant exact travelling wave solutions of these equations are obtained, which include the soliton, the hyperbolic function, the trigonometric function, and the rational functions. Also it is shown that the proposed method is efficient for solving nonlinear evolution equations in mathematical physics and in engineering.

scholarly journals New Exact Solutions for New Model Nonlinear Partial Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
A. Maher ◽  
H. M. El-Hawary ◽  
M. S. Al-Amry
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Elliptic Functions ◽  
Rational Functions ◽  
Travelling Wave ◽  
Mapping Method ◽  
Travelling Wave Solutions ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
New Exact Solutions ◽  
New Form

In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.

scholarly journals The(G′/G)-Expansion Method and Its Application for Higher-Order Equations of KdV (III)

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huizhang Yang ◽  
Wei Li ◽  
Biyu Yang
Keyword(s):  
Traveling Wave ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Higher Order ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Wave Solutions ◽  
Linear Differential

New exact traveling wave solutions of a higher-order KdV equation type are studied by the(G′/G)-expansion method, whereG=G(ξ)satisfies a second-order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. The property of this method is that it is quite simple and understandable.

Three Kind of Triangle Rational Functions and Applications for Discrete Nonlinear Equations

2011 ◽  
Vol 317-319 ◽  
pp. 2168-2171
Author(s):  
Xiu Rong Guo ◽  
Zheng Tao Liu ◽  
Mei Guo
Keyword(s):  
Nonlinear Equations ◽  
Difference Equations ◽  
Soliton Solutions ◽  
Rational Functions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Periodic Travelling Wave ◽  
Formal Solutions

In order to efficiently search for new soliton solutions to differential-difference equations (DDEs), three kinds of triangle rational functions are first introduced. Then a kind of formal solutions of DDEs are presented which are expressed by a unified nonlinear combination of the three kinds of triangle rational functions. As illustrative examples, the periodic travelling-wave solutions of the discrete modified KdV(mKdV) equations are obtained.

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