Solitary water wave interactions for the Forced Korteweg-de Vries equation

TL;DR

This paper investigates how solitary water waves interact over topographic obstacles within the forced Korteweg-de Vries equation, revealing regimes of stable interactions and extending classical KdV soliton interaction classifications.

Contribution

It analyzes solitary wave interactions in the fKdV, identifying regimes of crest separation and confirming the applicability of KdV interaction laws to the forced case.

Findings

Regimes where two crests remain separated during interaction

Transitions between one and two maxima following specific laws

Lax-categorization of KdV interactions applies to fKdV

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.