scholarly journals Exact Traveling Wave Solutions to the (2 + 1)-Dimensional Jaulent-Miodek Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yongyi Gu ◽  
Bingmao Deng ◽  
Jianming Lin
Keyword(s):  
Differential Equations ◽  
Computer Simulations ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Complex Method ◽  
Exact Traveling Wave Solutions ◽  
Applied Method ◽  
Wave Solutions

We derive exact traveling wave solutions to the (2 + 1)-dimensional Jaulent-Miodek equation by means of the complex method, and then we illustrate our main result by some computer simulations. It has presented that the applied method is very efficient and is practically well suited for the nonlinear differential equations that arise in mathematical physics.

scholarly journals Integrability via Functional Expansion for the KMN Model

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1819
Author(s):  
Radu Constantinescu ◽  
Aurelia Florian
Keyword(s):  
Differential Equations ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Auxiliary Equation ◽  
First Order ◽  
Second Order Differential Equations ◽  
Functional Expansion ◽  
Wave Solutions ◽  
First Time

This paper considers issues such as integrability and how to get specific classes of solutions for nonlinear differential equations. The nonlinear Kundu–Mukherjee–Naskar (KMN) equation is chosen as a model, and its traveling wave solutions are investigated by using a direct solving method. It is a quite recent proposed approach called the functional expansion and it is based on the use of auxiliary equations. The main objectives are to provide arguments that the functional expansion offers more general solutions, and to point out how these solutions depend on the choice of the auxiliary equation. To see that, two different equations are considered, one first order and one second order differential equations. A large variety of KMN solutions are generated, part of them listed for the first time. Comments and remarks on the dependence of these solutions on the solving method and on form of the auxiliary equation, are included.

scholarly journals Further Results about Traveling Wave Exact Solutions of the Drinfeld-Sokolov Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Fu Zhang ◽  
Jian-ming Qi ◽  
Wen-jun Yuan
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Complex Method ◽  
Wave Solutions ◽  
Periodic Traveling Wave

We employ the complex method to obtain all meromorphic exact solutions of complex Drinfeld-Sokolov equations (DS system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all constant and simply periodic traveling wave exact solutions of the equations (DS) are solitary wave solutions, the complex method is simpler than other methods and there exist simply periodic solutionsvs,3(z)which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.

scholarly journals A Note on the Fractional Generalized Higher Order KdV Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Yongyi Gu
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Nonlinear Differential Equations ◽  
Mathematical Physics ◽  
Higher Order ◽  
Complex Method ◽  
Applied Method ◽  
De Vries

We obtain exact solutions to the fractional generalized higher order Korteweg-de Vries (KdV) equation using the complex method. It has showed that the applied method is very useful and is practically well suited for the nonlinear differential equations, those arising in mathematical physics.

Exact traveling wave solutions of partial differential equations with power law nonlinearity

2015 ◽  
Vol 4 (3) ◽  
Author(s):  
H. Aminikhah ◽  
B. Pourreza Ziabary ◽  
H. Rezazadeh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Hyperbolic Function ◽  
Mathematical Tool ◽  
Partial Differential ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

AbstractIn this paper, we applied the functional variable method for four famous partial differential equations with power lawnonlinearity. These equations are included the Kadomtsev-Petviashvili, (3+1)-Zakharov-Kuznetsov, Benjamin-Bona-Mahony-Peregrine and Boussinesq equations. Various exact traveling wave solutions of these equations are obtained that include the hyperbolic function solutions and the trigonometric function solutions. The solutions shown that this method provides a very effective, simple and powerful mathematical tool for solving nonlinear equations in various fields of applied sciences.

scholarly journals Exact Traveling Wave Solutions to Benney- Luke Equation

2018 ◽  
Vol 37 ◽  
pp. 1-14
Author(s):  
Zahidul Islam ◽  
Mohammad Mobarak Hossain ◽  
Md Abu Naim Sheikh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Sobolev Type ◽  
Travelling Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

By using the improved (G¢/G) -expansion method, we obtained some travelling wave solutions of well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation. We show that the improved (G¢/G) -expansion method is a useful, reliable, and concise method to solve these types of equations.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 1-14

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