Eur. Phys. J. Plus (2021) 136: 980
https://doi.org/10.1140/epjp/s13360-021-01924-9

Regular Article

Breaking analysis of solitary waves for the shallow water wave system in fluid dynamics

¹ Department of Mathematics and Science Education, Faculty of Education, Adıyaman University, 02040, Adiyaman, Turkey
² Department of Mathematics, Istanbul Commerce University, 34445, Istanbul, Turkey

^a sduran@adiyaman.edu.tr

Received: 14 March 2021
Accepted: 31 August 2021
Published online: 28 September 2021

Abstract

Analytical solutions and physical interpretations for the shallow water wave system, which is the modeling of a physical phenomenon in applied mathematics, are presented in this study. The solutions of the shallow water wave system, which models the formation, interaction and breaking of shallow water waves on the ocean surface as a result of external effects (e.g., wind), are examined using the modified expansion method. Besides, physically, the differences between deep and shallow water waves and their transitions with each other are examined. Hyperbolic and trigonometric wave solutions are produced with the advantages of the modified expansion method over other traditional methods. In these wave solutions, the values that cause the breaking of the wave are calculated by considering the velocity parameter. The behavior of the wave at these values is presented with the help of simulations. Finally, the states of solitary wave solutions concerning each other in the same system are compared and analyzed according to the velocity parameter.