Dark solitons in a Gross–Pitaevskii equation with a power-law nonlinearity: application to ultracold Fermi gases near the Bose–Einstein condensation regime

Abstract

In this work, we consider a model of a defocusing nonlinear Schrödinger equation with a variable nonlinearity exponent. This is motivated by the study of a superfluid Fermi gas in the Bose–Einstein condensation (BEC)–Bardeen–Cooper–Schrieffer crossover. In particular, we focus on the relevant mean-field model in the regime from BEC to unitarity and especially consider the modification of the nearly black soliton oscillation frequency due to the variation in the nonlinearity exponent in a harmonic trapping potential. The analytical expressions given as a function of the relevant nonlinearity exponent are corroborated by numerical computations and also extended past the BEC limit.