Solitary and periodic wave solutions to the family of new 3D fractional WBBM equations in mathematical physics

Abdulla-Al Mamun; Nur Hasan Mahmud Shahen; Samsun Nahar Ananna; Md Asaduzzaman; Foyjonnesa

doi:10.1016/j.heliyon.2021.e07483

Solitary and periodic wave solutions to the family of new 3D fractional WBBM equations in mathematical physics

Heliyon. 2021 Jul 7;7(7):e07483. doi: 10.1016/j.heliyon.2021.e07483. eCollection 2021 Jul.

Authors

Abdulla-Al Mamun^{1

2}, Nur Hasan Mahmud Shahen³, Samsun Nahar Ananna^{1

2}, Md Asaduzzaman², Foyjonnesa³

Affiliations

¹ Department of Mathematics, College of Science, Hohai University, Nanjing-210098, PR China.
² Department of Mathematics, Islamic University, Kushtia-7003, Bangladesh.
³ Department of Mathematics, European University of Bangladesh, Dhaka-1216, Bangladesh.

Abstract

For the newly implemented 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equation family, the present study explores the exact singular, solitary, and periodic singular wave solutions via the ( $G^{'} / G^{2}$ )-expansion process. In the sense of conformable derivatives, the equations considered are translated into ordinary differential equations. In spite with many trigonometric, complex hyperbolic, and rational functions, some fresh exact singular, solitary, and periodic wave solutions to the deliberated equations in fractional systems are attained by the implementation of the ( $G^{'} / G^{2}$ )-expansion technique through the computational software Mathematica. The unique solutions derived by the process defined are articulated with the arrangement of the functions tanh, sech; tan, sec; coth, cosech, and cot, cosec. With three-dimensional (3D), two dimensional (2D) and contour graphics, some of the latest solutions created have been envisaged, selecting appropriate arbitrary constraints to illustrate their physical representation. The outcomes were obtained to determine the power of the completed technique to calculate the exact solutions of the equations of the WBBM that can be used to apply the nonlinear water model in the ocean and coastal engineering. All the solutions given have been certified by replacing their corresponding equations with the computational software Mathematica.

Keywords: ( G ′ / G 2 ) -expansion method; Conformable derivative; Exact solution; Shallow water wave; Wazwaz-Benjamin-Bona-Mahony equation.