Generalized Exp-Function Method to Find Closed Form Solutions of Nonlinear Dispersive Modified Benjamin–Bona–Mahony Equation Defined by Seismic Sea Waves

Muhammad Shakeel, Attaullah, Essam Roshdy El-Zahar, Nehad Ali Shah and Jae Dong Chung
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Muhammad Shakeel: Department of Mathematics, University of Wah, Wah Cantt 47040, Pakistan
Attaullah: Department of Mathematics, University of Wah, Wah Cantt 47040, Pakistan
Essam Roshdy El-Zahar: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi Arabia
Nehad Ali Shah: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
Jae Dong Chung: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea

Mathematics, 2022, vol. 10, issue 7, 1-17

Abstract: Using the new generalized exp-function method, we were able to derive significant novel closed form solutions to the nonlinear dispersive modified Benjamin–Bona–Mahony (DMBBM) equation. The general framework of the new generalized exp-function method has been given. Many novel closed form solutions have been obtained in the form of hyperbolic, trigonometric, and rational function solutions. Using the computer application Wolfram Mathematica 10, we plotted 2D, 3D, and contour surfaces of closed form solutions found in this work. In the form of a table, the acquired results are compared to the known solutions in the existing literature.

Keywords: generalized exp (? ? ( ? )) expansion method; exact solutions; nonlinear dispersive modified Benjamin–Bona–Mahony equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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