Decay of Kadomtsev-Petviashvili solitons

Abstract

The Kadomtsev-Petviashvili equation with positive dispersion has well known flat as well as two dimensional soliton solutions. The two dimensional solitons, however, involve regions of depressed as well as of excess density. It might therefore seem to be an open question if flat solitons, known to be unstable, would decompose into these rather strange structures. The present paper definitely answers this question in the affirmative by describing a numerical simulation.