Extreme elevations and slopes of interacting solitons in shallow water

The paper describes a nonlinear phenomenon of interaction of waves that may be a reason for the existence of high-amplitude wave humps on the sea surface. The properties of extreme elevation area in the vicinity of the intersection point of two long-crested shallow water waves travelling in slightly different directions are evaluated in the framework of two-soliton solution of the Kadomtsev-Petviashvili equation. The extent of the area where surface elevation exceeds a certain level is estimated analytically based on the study of corresponding surface isolines. Shown is that this area is very narrow in the direction of its propagation. The extreme slopes at the front of the interaction soliton may eight times exceed the maximum slope of the interacting solitons.