Abstract:The energy-velocity relation of a dark soliton is usually derived by its exact solution, which has been used to explain the kinetic motion of dark soliton widely in many-body physical systems. We perform a variational method to re-derive the dispersion relation, with considering the dark soliton's particle number could be conserved. The re-derived dispersion relation is completely different from the one given by exact dark soliton solution. The validity of these two dispersion relations is tested by observing … Show more
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