Surface wave behavior and refraction simulation on the ocean for the fractional Ostrovsky–Benjamin–Bona–Mahony equation

Abstract

In this study, we have taken into account the time-fractional Ostrovsky–Benjamin–Bona–Mahony equation, which is a synthesis of the time-fractional Ostrovsky equation and time-fractional Benjamin–Bona–Mahony equations and contains both mathematical and physical properties. Traveling wave solutions are produced by using the Ostrovsky–Benjamin–Bona–Mahony equation that physically sheds light on the incoming wave event on the ocean surface, using the sub-equation and Bernoulli sub-equation function methods. These solutions are presented in hyperbolic, trigonometric, singular and dark (topological) soliton types. With the help of special values given to the coefficients in the solitons obtained, it is associated with the solutions in the literature and it is observed that the solitons produced in this study are more general. Graphs representing the stationary wave at any given moment are presented. The advantages and disadvantages as well as the similarities and differences of the method are discussed in detail. Also, the behavior of the wave and its refraction according to the velocity variable, which is a physically important factor of the traveling wave solution, is analyzed and supported by simulation.