Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics

Abstract

In this study, analytical solutions and physical interpretations are presented for the Riemann wave equation (RWE), which has an important physical property in fluid dynamics. The solutions of the RWE, which models the formation, interaction and breaking of the waves that occur as a result of any external effect on the ocean surface, are examined using the generalized exponential rational function method (GERFM). Bright (nontopological) soliton, singular soliton and solitary wave solutions are produced with advantages of GERFM over other traditional exponential methods. The factors in which solitary wave solutions cause breaking of wave are examined. The effects of parameters on wavefunctions and the physical interpretations of these effects are discussed and supported by graphics and simulations.