International Journal of Scientific Engineering and Technology

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Traveling Wave Solutions for the Foam Drainage Equation and the Enhanced (G'/G)-Expansion Method


Affiliations
1 Department of Mathematics, Pabna University of Science & Technology, Pabna-6600, Bangladesh
2 Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science & Technology University, Gopalgang-8100, Bangladesh
3 Department of Mathematics & Statistics, Jessore University of Science & Technology, Jessore-7408, Bangladesh
 

In this paper, the enhanced (G'/G)-expansion method is used to assemble the traveling wave solutions involving parameters of the Foam Drainage equation, where G=G(ξ) satisfies a second order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. When some arbitrary functions included in these solutions are taken as some special functions, these solutions possess profuse structures. This method is direct, concise elementary and effective and can be used for many other nonlinear evolutions equations.

Keywords

Enhanced (G'/G)-Expansion Method, Foam Drainage Equation, NLEEs, Traveling Wave Solutions, Solitary Waves.
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  • Traveling Wave Solutions for the Foam Drainage Equation and the Enhanced (G'/G)-Expansion Method

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Authors

S. M. Rayhanul Islam
Department of Mathematics, Pabna University of Science & Technology, Pabna-6600, Bangladesh
M. Shuzon Ali
Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science & Technology University, Gopalgang-8100, Bangladesh
M. Shaiful Islam
Department of Mathematics & Statistics, Jessore University of Science & Technology, Jessore-7408, Bangladesh
Kamruzzaman Khan
Department of Mathematics, Pabna University of Science & Technology, Pabna-6600, Bangladesh

Abstract


In this paper, the enhanced (G'/G)-expansion method is used to assemble the traveling wave solutions involving parameters of the Foam Drainage equation, where G=G(ξ) satisfies a second order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. When some arbitrary functions included in these solutions are taken as some special functions, these solutions possess profuse structures. This method is direct, concise elementary and effective and can be used for many other nonlinear evolutions equations.

Keywords


Enhanced (G'/G)-Expansion Method, Foam Drainage Equation, NLEEs, Traveling Wave Solutions, Solitary Waves.