Lump Collision Phenomena to a Nonlinear Physical Model in Coastal Engineering

Tukur Abdulkadir Sulaiman, Abdullahi Yusuf (), Ali Saleh Alshomrani and Dumitru Baleanu
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Tukur Abdulkadir Sulaiman: Department of Computer Engineering, Biruni University, Istanbul 34010, Turkey
Abdullahi Yusuf: Department of Computer Engineering, Biruni University, Istanbul 34010, Turkey
Ali Saleh Alshomrani: Department of Mathematics, King Abdul Aziz University, Jeddah 21589, Saudi Arabia
Dumitru Baleanu: Department of Mathematics, Cankaya University, Ankara 06530, Turkey

Mathematics, 2022, vol. 10, issue 15, 1-10

Abstract: In this study, a dimensionally nonlinear evolution equation, which is the integrable shallow water wave-like equation, is investigated utilizing the Hirota bilinear approach. Lump solutions are achieved by its bilinear form and are essential solutions to various kind of nonlinear equations. It has not yet been explored due to its vital physical significant in various field of nonlinear science. In order to establish some more interaction solutions with some novel physical features, we establish collision aspects between lumps and other solutions by using trigonometric, hyperbolic, and exponential functions. The obtained novel types of results for the governing equation includes lump-periodic, two wave, and breather wave solutions. Meanwhile, the figures for these results are graphed. The propagation features of the derived results are depicted. The results reveal that the appropriate physical quantities and attributes of nonlinear waves are related to the parameter values.

Keywords: shallow water wave-like scalar equation; Hirota bilenear method; breather wave solution; lump-periodic solution; two-wave solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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