Dynamics of interaction between solitary and rogue wave of the space-time fractional Broer–Kaup models arising in shallow water of harbor and coastal zone

Abstract

Under inquisition, we consider the space-time fractional Broer–Kaup model that replicate the real coastal profile to describe bidirectional wave transmission of long waves in shallow water. We integrate of the model via the unified scheme to derive exact solitary wave solutions. The achieved results present the hyperbolic, trigonometric, and rational functions solutions. All of these solutions convey the periodic and solitonic natures. In particular, we present combo waves that imply a curvy periodic waves in which rogue waves occur in both sides of each waves. The dynamics of obtained nonlinear wave solutions are demonstrated in 3-D and 2-D shapes with definite parametric values. It is shown that the obtained solutions of the model pact a very rich dynamical behavior and can be used to describe seismic type nonlinear wave motion in shallow water waves of the coastal and harbor region.