Breakup of two-dimensional into three-dimensional Kadomtsev-Petviashvili solitons

Abstract

This paper reports on three-dimensional simulations that follow exact, $z$-symmetric soliton solutions to an important model equation of plasma physics and superfluid helium (Bose condensate). This is the Kadomtsev-Petviashvili equation. Solitons are seen to break up when perturbed along $z$. Dependence of growth on the wave number of the perpendicular perturbation is found numerically. This leads to a wave number producing the maximum rate of breakup. Due to numerical instabilities, a somewhat smaller wave number must be used. Fully three-dimensional entities are produced. After a while they become virtually identical to known, azimuthally symmetric solutions. Based on this, implications for the reconnection hypothesis formulated by Feynman, used in superfluid helium II theory, are indicated.