Soliton interactions with an external forcing: the modified Korteweg-de Vries framework

TL;DR

This paper investigates how solitons interact with external forces of variable speed within the forced mKdV framework, revealing trapping phenomena and amplitude changes depending on the forcing's acceleration or deceleration.

Contribution

It provides the first combined asymptotic and numerical analysis of soliton interactions with variable-speed external forcing in the mKdV equation.

Findings

Asymptotic predictions match numerical solutions for constant and linear variable speeds.

Solitons can become trapped at the external forcing under certain conditions.

Amplitude of solitons increases or decreases depending on the forcing's acceleration or deceleration.

Abstract

The aim of this work is to study asymptotically and numerically the interaction of solitons with an external forcing with variable speed using the forced modified Korteweg-de Vries equation (mKdV). We show that the asymptotic predictions agree well with numerical solutions for forcing with constant speed and linear variable speed. Regarding forcing with linear variable speed, we find regimes in which the solitons are trapped at the external forcing and its amplitude increases or decreases in time depending on whether the forcing accelerates or decelerates.