Solitons in two-dimensional Bose-Einstein condensates

TL;DR

This paper investigates the excitations of a two-dimensional Bose-Einstein condensate with solitons, revealing localized resonant states near the soliton that behave like coupled oscillations, using the Kadomtsev-Petviashvili equation.

Contribution

It introduces a detailed analysis of soliton excitations in 2D BECs and demonstrates their resonant nature through the stabilization method.

Findings

Localized excitation states near the soliton with dispersion similar to transverse oscillations.

Resonant states are coupled to the continuum of free excitations.

The Kadomtsev-Petviashvili equation effectively describes soliton dynamics in 2D BECs.

Abstract

The excitations of a two-dimensional (2D) Bose-Einstein condensate in the presence of a soliton are studied by solving the Kadomtsev-Petviashvili equation which is valid when the velocity of the soliton approaches the speed of sound. The excitation spectrum is found to contain states which are localized near the soliton and have a dispersion law similar to the one of the stable branch of transverse oscillations of a 1D gray soliton in a 2D condensate. By using the stabilization method we show that these localized excitations behave as resonant states coupled to the continuum of free excitations of the condensate.