Describing Water Wave Propagation Using the G ′ G 2 –Expansion Method

Safoura Rezaei Aderyani, Reza Saadati (), Donal O’Regan and Fehaid Salem Alshammari
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Safoura Rezaei Aderyani: School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran
Reza Saadati: School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran
Donal O’Regan: School of Mathematical and Statistical Sciences, University of Galway, University Road, H91 TK33 Galway, Ireland
Fehaid Salem Alshammari: Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11432, Saudi Arabia

Mathematics, 2022, vol. 11, issue 1, 1-24

Abstract: In the present study, our focus is to obtain the different analytical solutions to the space–time fractional Bogoyavlenskii equation in the sense of the Jumaries-modified Riemann–Liouville derivative and to the conformable time–fractional-modified nonlinear Schrödinger equation that describes the fluctuation of sea waves and the propagation of water waves in ocean engineering, respectively. The G ′ G 2 –expansion method is applied to investigate the dynamics of solitons in relation to governing models. Moreover, the restriction conditions for the existence of solutions are reported. In addition, we note that the accomplished solutions are useful to the description of wave fluctuation and the wave propagation survey and are also significant for experimental and numerical verification in ocean engineering.

Keywords: Jumaries-modified Riemann-Liouville derivative; conformable time-modified nonlinear Schrödinger equation; space–time fractional Bogoyavlenskii equation; G ? G 2 –expansion method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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