A simple model of radiating solitary waves

TL;DR

This paper introduces a simplified model that captures the behavior of radiating solitary waves, showing their amplitude decays exponentially with a very slow decay rate, and provides a complete analytical understanding using Laplace transforms.

Contribution

The paper presents a minimalistic analytical model for radiating solitary waves, enabling complete analysis and revealing the exponential decay dynamics of wave amplitude.

Findings

Wave amplitude decays exponentially over time.

Decay constant can be extremely small, beyond all orders of frequency.

Model captures essential features of radiating solitary waves.

Abstract

To understand an oft-observed but poorly understood phenomenon in which a solitary wave in a dispersive equation slowly deteriorates due to a persistent emission of radiation (i.e. a ``radiating solitary wave''), we propose a bare-bones model which captures many essential features and which we are capable of analyzing completely by way of the Laplace transform. We find that wave amplitude decreases at an exponential rate but with a decay constant that is (in many cases) small beyond all orders of the frequency.