Document Type : Research Paper
Authors
1
Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt.
2
Department of Physics and Engineering Mathematics, Faculty of Engineering, Ain Shams University Abbassia, Cairo, Egypt.
3
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt.
4
Department of Mathematics, Faculty of Science, Luxor University, Taiba, Luxor, Egypt.
5
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
6
Department of Engineering Sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan, Rudsar-Vajargah, P.C. 44891-63157, Iran.
Abstract
A lot of people employ nonlinear evolution equations to figure out the fundamentals of natural phenomena. The study of nonlinear equations in depth is a component of the non-linear sciences, which also include fluid dynamics, ocean physics, plasma physics, and applications in the field of marine engineering. Using the extended F-expansion approach, this paper investigates the generalized non-linear (3+1)-dimensional wave equation under the effect of conformable fractional derivative (CFD) and finds numerous exact time-fractional wave solutions as well as the fluctuating dynamics of various wave profiles. This work explains other non-linear phenomena in liquids, such as gas bubbles. Unique soliton waves exhibit dynamical behavior involving several soliton solutions, including singular, bright, and dark. Additionally, periodic and singular periodic wave profiles are acquired. We could not find any previous publications of these found solutions. Using two- and three-dimensional graphics and associated contour plots, the dynamical wave structures of some analytical solutions can be graphically represented by assigning appropriate values to free parameters. Furthermore, this method can be used to find soliton solutions of other well-known equations in fluid dynamics, engineering physics, and other nonlinear fields.
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