On the Conversion of Partial Differential Equations

2010 ◽  
Vol 65 (11) ◽  
pp. 896-900 ◽  
Author(s):  
Syed Tauseef Mohyud-Din
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Function Method ◽  
Homotopy Perturbation Method ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Homotopy Perturbation ◽  
Wave Solutions ◽  
Complex Transformation

This paper outlines the conversion of partial differential equations (PDEs) into the corresponding ordinary differential equations (ODEs) by a complex transformation which is widely used in the exp-function method. The proposed homotopy perturbation method (HPM) is employed to solve the travelling wave solutions. Several examples are given to reveal the reliability and efficiency of the algorithm.

Extended tanh-Function Method for Finding Travelling Wave Solutions of Some Nonlinear Partial Differential Equations

2005 ◽  
Vol 60 (1-2) ◽  
pp. 7-16 ◽  
Author(s):  
Mustafa Inc ◽  
Engui G. Fan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Nonlinear Pdes ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions

In this paper, we find travelling wave solutions of some nonlinear partial differential equations (PDEs) by using the extended tanh-function method. Some illustrative equations are investigated by this method and new travelling wave solutions are found. In addition, the properties of these nonlinear PDEs are shown with some figures.

Exact Travelling Wave Solutions of Toda Lattice Equations Obtained via the Exp-Function Method

2008 ◽  
Vol 63 (10-11) ◽  
pp. 657-662 ◽  
Author(s):  
Chao-Qing Dai ◽  
Yue-Yue Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Function Method ◽  
Toda Lattice ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions ◽  
Toda Lattices

We generalize the exp-function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we study two Toda lattices and obtain some new travelling wave solutions by means of the exp-function method. As some special examples, some new exact travelling wave solutions can degenerate into the kink-type solitary wave solutions reported in open literatures.

scholarly journals Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Haci Mehmet Baskonus ◽  
Mustafa Kayan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Function Method ◽  
Travelling Wave ◽  
Bright Soliton ◽  
Travelling Wave Solutions ◽  
New Wave ◽  
Partial Differential ◽  
Wave Solutions ◽  
Fifth Order

Abstract This paper applies a powerful scheme, namely Bernoulli sub-equation function method, to some partial differential equations with high non-linearity. Many new travelling wave solutions, such as mixed dark-bright soliton, exponential and complex domain, are reported. Under a suitable choice of the values of parameters, wave behaviours of the results obtained in the paper – in terms of 2D, 3D and contour surfaces – are observed.

New Soliton Solutions of Chaffee-Infante Equations Using the Exp-Function Method

2010 ◽  
Vol 65 (3) ◽  
pp. 197-202 ◽  
Author(s):  
Rathinasamy Sakthivel ◽  
Changbum Chun
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symbolic Computation ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

In this paper, the exp-function method is applied by using symbolic computation to construct a variety of new generalized solitonary solutions for the Chaffee-Infante equation with distinct physical structures. The results reveal that the exp-function method is suited for finding travelling wave solutions of nonlinear partial differential equations arising in mathematical physics

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