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Dynamics of shallow dark solitons in a trapped gas of impenetrable bosons

D. J. Frantzeskakis·N. P. Proukakis·P. G. Kevrekidis
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Abstract

The dynamics of linear and nonlinear excitations in a Bose gas in the Tonks-Girardeau (TG) regime with longitudinal confinement are studied within a mean field theory of quintic nonlinearity. A reductive perturbation method is used to demonstrate that the dynamics of shallow dark solitons, in the presence of an external potential, can effectively be described by a variable-coefficient Korteweg-de Vries equation. The soliton oscillation frequency is analytically obtained to be equal to the axial trap frequency, in agreement with numerical predictions obtained by Busch {\it et al.} [J. Phys. B {\bf 36}, 2553 (2003)] via the Bose-Fermi mapping. We obtain analytical expressions for the evolution of both soliton and emitted radiation (sound) profiles.

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D. J. Frantzeskakis, N. P. Proukakis, P. G. Kevrekidis. 2004-04-05. Dynamics of shallow dark solitons in a trapped gas of impenetrable bosons. https://doi.org/10.1103/physreva.70.015601

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