A study on the compatibility of the generalized Kudryashov method to determine wave solutions

Hemonta Kumar Barman ^a, Md. Ekramul Islam ^b, M. Ali Akbar ^a,*

a. Department of Applied Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh
         b. Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh

Abstract: In this article, we establish solitary wave solutions to the Estevez-Mansfield-Clarkson (EMC) equation and the coupled sine-Gordon equations which are model equations to analyze the formation of shapes in liquid drops, surfaces of negative constant curvature, etc. through contriving the generalized Kudryashov method. The extracted results introduce several types’ solitary waves, such as the kink soliton, bell-shape soliton, compacton, singular soliton, peakon and other sort of soliton for distinct valuation of the unknown parameters. The achieved analytic solutions are interpreted in details and their 2D and 3D graphs are sketched. The obtained solutions and the physical structures explain the soliton phenomenon and reproduce the dynamic properties of the front of the traveling wave deformation generated in the dispersive media. It shows that the generalized Kudryashov method is powerful, compatible and might be used in further works to found novel solutions for other types of nonlinear evolution equations ascending in physical science and engineering.

Keywords: The nonlinear evolution equations (NLEEs); The Estevez-Mansfield-Clarkson (EMC) equation; The coupled sine-Gordon equations; The generalized Kudryashov method; Solitons; Analytic solutions