title: Matter-wave dark solitons: stochastic versus analytical results.
abstract: The dynamics of dark matter-wave solitons in elongated atomic condensates are discussed at finite temperatures. Simulations with the stochastic Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread in individual soliton trajectories, attributed to inherent fluctuations in both phase and density of the underlying medium. Averaging over a number of such trajectories (as done in experiments) washes out such background fluctuations, revealing a well-defined temperature-dependent temporal growth in the oscillation amplitude. The average soliton dynamics is well captured by the simpler dissipative Gross-Pitaevskii equation, both numerically and via an analytically derived equation for the soliton center based on perturbation theory for dark solitons.
authors.affiliation: School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom.
authors.forename: S P
authors.initials: SP
authors.lastname: Cockburn
authors.forename: H E
authors.initials: HE
authors.lastname: Nistazakis
authors.forename: T P
authors.initials: TP
authors.lastname: Horikis
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: N P
authors.initials: NP
authors.lastname: Proukakis
authors.forename: D J
authors.initials: DJ
authors.lastname: Frantzeskakis