scholarly journals A Modification of the Generalized Kudryashov Method for the System of Some Nonlinear Evolution Equations

2019 ◽  
Vol 14 (1) ◽  
Author(s):  
H. M. Shahadat Ali
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

scholarly journals Investigation of Dark and Bright Soliton Solutions of Some Nonlinear Evolution Equations

2018 ◽  
Vol 22 ◽  
pp. 01056 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Bright Soliton ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Ostrovsky Equation

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.

The shock peakon wave solutions of the general Degasperis–Procesi equation

2019 ◽  
Vol 33 (29) ◽  
pp. 1950351 ◽  
Author(s):  
Lijuan Qian ◽  
Raghda A. M. Attia ◽  
Yuyang Qiu ◽  
Dianchen Lu ◽  
Mostafa M. A. Khater
Keyword(s):  
Stability Property ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Dynamical Behavior ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Different Types ◽  
The Stability

This research paper applies the modified Khater method and the generalized Kudryashov method to the general Degasperis–Procesi (DP) equation, which is used to describe the dynamical behavior of the shallow water outflows. Some shock peakon wave solutions are obtained by using these methods. Moreover, some figures are sketched for these solutions to explain more physical properties of the general DP equation and to figure out the coincidence between different types of obtained solutions. The stability property by using the features of the Hamiltonian system is tested to some obtained solutions to show their ability for applying in the model’s applications. The obtained solutions were verified with Maple 16 & Mathematica 12 by placing them back into the original equations. The performance of these methods shows their power and effectiveness for applying to many different forms of the nonlinear evolution equations with an integer and fractional order.

scholarly journals New Wave Solutions for Nonlinear Differential Equations using an Extended Bernoulli Equation as a New Expansion Method

2018 ◽  
Vol 22 ◽  
pp. 01035
Author(s):  
Serbay DURAN ◽  
Doǧan KAYA
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Differential Equations ◽  
Expansion Method ◽  
Equation System ◽  
Nonlinear Evolution Equations ◽  
New Wave ◽  
Bernoulli Equation ◽  
Wave Solutions ◽  
Kudryashov Method

In this paper, we presented a new expansion method constructed by taking inspiration for the Kudryashov method. Bernoulli equation is chosen in the form of F′=BFn-AF and some expansions are made on the auxiliary Bernoulli equation which is used in this method. In this auxiliary Bernoulli equation some wave solutions are obtained from the shallow water wave equation system in the general form of “n-order”. The obtained new results are simulated by graphically in 3D and 2D. To sum up, it is considered that this method can be applied to the several of nonlinear evolution equations in mathematics physics.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

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