2022-04

CMES 2022

This study analyses the HSIE, which discusses the propagation of unidirectional shallow-water waves

2021-06

CMES

In this article, the sine-Gordon equation expansion method is used to find the analytical traveling wave solution of the (2+1)-dimensional resonant Davey-Stewartson equations system, which is a natural (2+1)-dimensional version of the resonant nonlinear Schröndinger equation. The imaginary (2+1)-dimensional resonant Davey-Stewatson system is converted into a system of nonlinear ordinary differential equations, after it the sine-Gordon method is applied, and the homogeneous balance between the order and the highest power of nonlinear terms of the ordinary differential equation is authorized. Finally, the outcomes equations are solved to achieve some new analytical solutions. For different cases as well as for different values of constants, the Wolfram Mathematica software is used to find novel solutions to the resulting system of the nonlinear differential equation. All new solutions of this study are plotted in 2D and 3D-dimensions graphically as well as verify the resonant Davey-Stewartson equations.

2019-07

International Conference on Mathematics and Mathematics Education

In this manuscript, we have applied the sine-Gordon expansion method and the Bernoulli sub-equation method to seek the traveling wave solutions of the (2+1)-dimensional time-fractional partial Zoomeron equation. The exact solutions of the Zoomeron equation that are obtained by the sine-Gordon method are plotted in 3D figures, as well as the effects of the fractional derivative α are illustrated in 2D figures, while the exact solutions of the Zoomeron equation that are obtained by the Bernoulli sub-equation method are plotted in 3D figures and contour plot. Bright solutions, kink soliton, singular soliton solution, and complex solutions to the studied equation are constructed. Also, different values of the fractional parameter α are tested to study the effect of the parameter. We conclude that these methods are sufficient for seeking the exact solutions.

2019-04

4th International Conference on Computational Mathematics and Engineering Sciences

In this article, by using the Bernoulli sub-equation, we build the analytical traveling wave solution of the (2+1)-dimensional Davey-Stewartson equation system. First of all, the imaginary (2+1)-dimensional Davey-Stewatson system is transformed into a system of nonlinear differential equations, After getting the resultant equation, the homogeneous method of balance between the highest power and the highest derivative of the ordinary differential equation is authorized and finally the outcomes equations are solved in order to achieve some new analytical solutions. Wolfram Mathematica Package is used for different cases as well as for different values of constants to investigate the solutions of the resulting system of a nonlinear differential equation. The results of this study are shown in 2D and 3D dimensions graphically.

2019-04

4th International Conference on Computational Mathematics and Engineering Sciences

The shallow water equations provide a vast range of applications in the ocean, atmospheric modeling, and pneumatic computing, which can also be utilized to modeling flows in rivers and coastal areas. The Bernoulli sub-equation function method is utilized to build the analytic solutions of the (1+1) dimensional coupled Whitham-Broer-Kaup (WBK) equations. This partial differential equation model is translated into ordinary differential equations in order to construct new exponential prototype structures. As a result, the novel results are obtained and then plotted in 3D and 2D surfaces.