Interactions of soliton and mean field in KdV equation with well type initial data

TL;DR

This paper investigates the interaction between solitons and mean fields in the KdV equation with well-type initial data, using Whitham modulation theory and numerical confirmation to analyze amplitude and phase changes.

Contribution

It applies Whitham modulation theory to describe soliton-mean field interactions in the KdV equation with well initial data, providing theoretical predictions verified numerically.

Findings

Identification of rarefaction and dispersion shock waves

Prediction of soliton amplitude and phase changes

Numerical confirmation of theoretical results

Abstract

For the KdV equation with well-type initial value, the interaction between the trial soliton and the mean field is studied. The well initial value will lead to the appearance of rarefaction wave and dispersion shock wave, and there will be a linear wave region after a long time. The interaction between trial soliton and mean field is described within the framework of Whitham modulation theory, and the trajectory of soliton is given. The predicted soliton amplitude and phase changes are numerically confirmed, verifying the correctness of the theoretical analysis.