A fractional Whitham-Broer-Kaup equation and its possible application to Tsunami prevention

Abstract

A fractional Whitham-Broer-Kaup equation is suggested using He?s fractional derivative to model solitary waves in shallow water in porous medium near a dam. A modification of the exp-function method, the generalized exponential rational function method, is adopted to elucidate the basic solution properties of the equation, revealing that the value of the fractional order can be used effectively to control the wave velocity, the wave height, and the wave morphology. This theoretical result can be used for possible tsunami prevention.