A simple model 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 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.