Simulations of Two-Dimensional Kadomtsev-Petviashvili Soliton Dynamics in Three-Dimensional Space

Abstract

This Letter reports on three-dimensional simulations that follow exact, $z$ symmetric soliton solutions to an important equation of plasma physics and fluid dynamics. These solitons are seen to break up when perturbed slightly along $z$. Some fairly robust, three-dimensional entities are subsequently produced. However, they do not seem to resemble known, azimuthally symmetric solutions. An explanation of this interesting fact is offered.