New Family of Solitary Wave Solutions to New Generalized Bogoyavlensky–Konopelchenko Equation in Fluid Mechanics

• Published in: International journal of applied and computational mathematics Vol. 9; no. 5
• Main Authors: Akram, Sonia, Ahmad, Jamshad, Rehman, Shafqat-Ur, Ali, Asghar
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.10.2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied mathematics; Computational mathematics; Computational Science and Engineering; Dynamic models; Fluid mechanics; Marine engineering; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nonlinear dynamics; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Plane waves; Solitary waves; Stability analysis; Theoretical; Improved; Stability analysis; Two-dimensional generalized Bogoyavlensky–Konopelchenko equation; Traveling wave soliton solutions; expansion method
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-023-01542-2

Many mathematicians and physicists are interested in Bogoyavlensky–Konopelchenko type equations to illustrate the various dynamics of nonlinear wave phenomena in the fields of fluid mechanics, hydrodynamics, and marine engineering. In this article, we investigate a new generalized (2+1)-dimensional Bogoyavlensky–Konopelchenko (gBK) equation analytically via the improved F -expansion function method and secure different solitary wave solutions in the form of dark, singular, periodic, and plane waves. Also, we discuss the stability analysis of our selected model, which confirms that the governing model is stable. To make this research more remarkable, we present the two-dimensional, three-dimensional, contour, and density graphs of particular solutions that were successfully produced in the accurate range space. The main objective of this study is to obtain the different kinds of solitary wave solutions of (2+1) gBK that are absent in the literature and justify the novelty of this study. We believe that these novel solutions hold a prominent place in the fields of fluid mechanics, engineering, and physics because they will enable a thorough understanding of the development and dynamic nature of such models. The achieved results are new and suggest that the applied method can also be implemented to handle other nonlinear dynamical models that arise in other disciplines of applied sciences.