Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations

A generalized(G′/G)-expansion method is proposed to seek the exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the Zakharov equations. As a result, some new Jacobi elliptic function solutions of the Zakharov equations are obtained. This method can also be applied to other nonlinear evolution equations in mathematical physics.

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Solving solitary wave solutions of higher dimensional nonlinear evolution equations with the homotopy analysis method

Acta Physica Sinica ◽

10.7498/aps.56.6791 ◽

2007 ◽

Vol 56 (12) ◽

pp. 6791

Author(s):

物理学报

Keyword(s):

Solitary Wave ◽

Homotopy Analysis Method ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Nonlinear Evolution Equations ◽

Solitary Wave Solutions ◽

Analysis Method ◽

Wave Solutions ◽

Higher Dimensional ◽

Homotopy Analysis

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Some Methods about Finding the Exact Solutions of Nonlinear Modified BBM Equation

Mathematical Problems in Engineering ◽

10.1155/2021/5564162 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Fan Niu ◽

Jianming Qi ◽

Zhiyong Zhou

Keyword(s):

Exact Solutions ◽

Rational Function ◽

Elliptic Function ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Mathematical Physics ◽

Nonlinear Evolution Equations ◽

Complex Method ◽

First Time ◽

Bbm Equation

Finding exact solutions of nonlinear equations plays an important role in nonlinear science, especially in engineering and mathematical physics. In this paper, we employed the complex method to get eight exact solutions of the modified BBM equation for the first time, including two elliptic function solutions, two simply periodic solutions, and four rational function solutions. We used the exp − ϕ z -expansion methods to get fourteen forms of solutions of the modified BBM equation. We also used the sine-cosine method to obtain eight styles’ exact solutions of the modified BBM equation. Only the complex method can obtain elliptic function solutions. We believe that the complex method presented in this paper can be more effectively applied to seek solutions of other nonlinear evolution equations.

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Application of the Subequation Method to Some Differential Equations of Time-Fractional Order

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4028826 ◽

2015 ◽

Vol 10 (5) ◽

Cited By ~ 11

Author(s):

Ahmet Bekir ◽

Esin Aksoy

Keyword(s):

Differential Equations ◽

Exact Solutions ◽

Fractional Order ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Nonlinear Evolution Equations ◽

New Exact Solutions

The main goal of this paper is to develop subequation method for solving nonlinear evolution equations of time-fractional order. We use the subequation method to calculate the exact solutions of the time-fractional Burgers, Sharma–Tasso–Olver, and Fisher's equations. Consequently, we establish some new exact solutions for these equations.

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A Novel Analytical Technique to Obtain Kink Solutions for Higher Order Nonlinear Fractional Evolution Equations

Abstract and Applied Analysis ◽

10.1155/2014/213482 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Qazi Mahmood Ul Hassan ◽

Jamshad Ahmad ◽

Muhammad Shakeel

Keyword(s):

Differential Equation ◽

Exact Solutions ◽

Fractional Derivatives ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Nonlinear Evolution Equations ◽

Fractional Evolution Equations ◽

Analytical Technique ◽

Fractional Complex Transform ◽

Fifth Order

We use the fractional derivatives in Caputo’s sense to construct exact solutions to fractional fifth order nonlinear evolution equations. A generalized fractional complex transform is appropriately used to convert this equation to ordinary differential equation which subsequently resulted in a number of exact solutions.

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