On the solution of the nonlinear Korteweg–de Vries equation by the homotopy perturbation method

2009 ◽  
Vol 25 (12) ◽  
pp. 1127-1136 ◽  
Author(s):  
Ahmet Yildirim
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Vries Equation ◽  
Homotopy Perturbation ◽  
De Vries

The Homotopy Perturbation Method for Solving the Modified Korteweg-de Vries Equation

2008 ◽  
Vol 63 (10-11) ◽  
pp. 621-626 ◽  
Author(s):  
Ahmet Yildirim
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Vries Equation ◽  
Nonlinear Differential Equations ◽  
Convergent Series ◽  
Science And Engineering ◽  
Weak Nonlinearity ◽  
Homotopy Perturbation ◽  
Engineering Problems ◽  
De Vries

The homotopy perturbation method (HPM) is employed successfully for solving the modified Korteweg-de Vries equation. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions or perturbation theory. The results show applicability, accuracy and efficiency of the HPM in solving nonlinear differential equations. It is predicted that the HPM can be widely applied in science and engineering problems.

Extension of the Homotopy Perturbation Method for Solving Nonlinear Differential-Difference Equations

2010 ◽  
Vol 65 (12) ◽  
pp. 1060-1064 ◽  
Author(s):  
Mohamed Medhat Mousa ◽  
Aidarkan Kaltayev ◽  
Hasan Bulut
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Difference Equations ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Lattice Equation ◽  
Convenient Tool ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
De Vries

In this paper, we have extended the homotopy perturbation method (HPM) to find approximate analytical solutions for some nonlinear differential-difference equations (NDDEs). The discretized modified Korteweg-de Vries (mKdV) lattice equation and the discretized nonlinear Schr¨odinger equation are taken as examples to demonstrate the validity and the great potential of the HPM in solving such NDDEs. Comparisons are made between the results of the presented method and exact solutions. The obtained results reveal that the HPM is a very effective and convenient tool for solving such kind of equations.

scholarly journals A local fractional homotopy perturbation method for solving the local fractional Korteweg-de Vries equations with non-homogeneous term

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1495-1501 ◽  
Author(s):  
Yong-Ju Yang ◽  
Shun-Qin Wang
Keyword(s):  
Perturbation Method ◽  
Initial Value Problems ◽  
Homotopy Perturbation Method ◽  
Validity And Reliability ◽  
Initial Value ◽  
Homotopy Perturbation ◽  
De Vries

In this paper, a local fractional homotopy perturbation method is presented to solve the boundary and initial value problems of the local fractional Korteweg-de Vries equations with non-homogeneous term. In order to demonstrate the validity and reliability of the method, two types of the Korteweg-de Vries equations with non-homogeneous term are proposed.

The Homotopy Perturbation Method for Solving Nonlinear Burgers and New Coupled Modified Korteweg-de Vries Equations

2008 ◽  
Vol 63 (10-11) ◽  
pp. 627-633 ◽  
Author(s):  
Elsayed M. E. Zayed ◽  
Taher A. Nofal ◽  
Khaled A. Gepreel
Keyword(s):  
Perturbation Method ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Travelling Wave ◽  
Systems Of Nonlinear Equations ◽  
Travelling Wave Solutions ◽  
Homotopy Perturbation ◽  
Wave Solutions ◽  
De Vries

We use the homotopy perturbation method to find the travelling wave solutions of nonlinear Burgers and new coupled modified Korteweg-de Vries equations. The results reveal that the homotopy perturbation method is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the homotopy perturbation method can find wide application in engineering and physics.

Solution of Fifth-order Korteweg and de Vries Equation by Homotopy perturbation Transform Method using He’s Polynomial

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Dinkar Sharma ◽  
Prince Singh ◽  
Shubha Chauhan
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Present Scheme ◽  
Homotopy Perturbation ◽  
Kdv Equations ◽  
De Vries ◽  
The Laplace Transform ◽  
Fifth Order

AbstractIn this paper, a combined form of the Laplace transform method with the homotopy perturbation method is applied to solve nonlinear fifth order Korteweg de Vries (KdV) equations. The method is known as homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He’s polynomials. Two test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM).

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