Solitary water wave interactions for the forced Korteweg–de Vries equation

Abstract

The aim of this work is to study solitary water wave interactions between two topographic obstacles for the forced Korteweg–de Vries equation (fKdV). Focusing on the details of the interactions, we identify regimes in which solitary wave interactions maintain two well separated crests and regimes where the number of local maxima varies according to the laws \(2\rightarrow 1\rightarrow 2\rightarrow 1\rightarrow 2\) or \(2\rightarrow 1\rightarrow 2\). It shows that the geometric Lax-categorization of Korteweg–de Vries (KdV) two-soliton interactions still holds for the fKdV equation.