scholarly journals Solitons and Other Exact Solutions for Two Nonlinear PDEs in Mathematical Physics Using the Generalized Projective Riccati Equations Method

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
A. M. Shahoot ◽  
K. A. E. Alurrfi ◽  
I. M. Hassan ◽  
A. M. Almsri
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Riccati Equations ◽  
Mathematical Physics ◽  
Nonlinear Pdes ◽  
Nls Equation ◽  
The Given ◽  
Order Dispersion

We apply the generalized projective Riccati equations method with the aid of Maple software to construct many new soliton and periodic solutions with parameters for two higher-order nonlinear partial differential equations (PDEs), namely, the nonlinear Schrödinger (NLS) equation with fourth-order dispersion and dual power law nonlinearity and the nonlinear quantum Zakharov-Kuznetsov (QZK) equation. The obtained exact solutions include kink and antikink solitons, bell (bright) and antibell (dark) solitary wave solutions, and periodic solutions. The given nonlinear PDEs have been derived and can be reduced to nonlinear ordinary differential equations (ODEs) using a simple transformation. A comparison of our new results with the well-known results is made. Also, we drew some graphs of the exact solutions using Maple. The given method in this article is straightforward and concise, and it can also be applied to other nonlinear PDEs in mathematical physics.

scholarly journals Study of coupled nonlinear partial differential equations for finding exact analytical solutions

2015 ◽  
Vol 2 (7) ◽  
pp. 140406 ◽  
Author(s):  
Kamruzzaman Khan ◽  
M. Ali Akbar ◽  
H. Koppelaar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Analytical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Partial Differential ◽  
Exact Analytical Solutions

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced ( G ′/ G )-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals First Integral Technique for Finding Exact Solutions of Higher Dimensional Mathematical Physics Models

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 783 ◽  
Author(s):  
Shumaila Javeed ◽  
Sidra Riaz ◽  
Khurram Saleem Alimgeer ◽  
M. Atif ◽  
Atif Hanif ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Dimensional Space ◽  
Nonlinear Partial Differential Equations ◽  
First Integral ◽  
Mathematical Physics ◽  
Space Time ◽  
Mathematical Tool ◽  
Long Wave ◽  
Higher Dimensional ◽  
Dimensional Space Time

In this work, we establish the exact solutions of some mathematical physics models. The first integral method (FIM) is extended to find the explicit exact solutions of high-dimensional nonlinear partial differential equations (PDEs). The considered models are: the space-time modified regularized long wave (mRLW) equation, the (1+2) dimensional space-time potential Kadomtsev Petviashvili (pKP) equation and the (1+2) dimensional space-time coupled dispersive long wave (DLW) system. FIM is a powerful mathematical tool that can be used to obtain the exact solutions of many non-linear PDEs.

scholarly journals On some nonlinear fractional PDEs in physics

BIBECHANA ◽  
2014 ◽  
Vol 12 ◽  
pp. 59-69
Author(s):  
Jamshad Ahmad ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Variational Iteration Method ◽  
Mathematical Physics ◽  
Inverse Transformation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Pdes ◽  
The Given ◽  
Nonlinear Nature

In this paper, we applied relatively new fractional complex transform (FCT) to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and Variational Iteration Method (VIM) is to find approximate solution of time- fractional Fornberg-Whitham and time-fractional Wu-Zhang equations. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs arising in mathematical physics and hence can be extended to other problems of diversified nonlinear nature. Numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the proposed algorithm.  DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11687BIBECHANA 12 (2015) 59-69 

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