Stationary hypergeometric solitons and their stability in a Bose-Einstein condensate with PT−symmetric potential

We report the existence of stationary nonlinear matter-waves in a trapped Bose-Einstein condensate subject to a PT−symmetric Pöschl-Teller potential with a gain/loss profile. Exact nonlinear modes are obtained and their stability criteria are determined. The analysis shows that beyond a critical depth of confining potential well, the condensate wavefunction is stable against small fluctuations in the field. Analytical results obtained are in good agreement with the numerical simulation of the localized modes in the PT symmetry regime. Employing the isospectral hamiltonian technique of supersymmetric quantum mechanics, we demonstrate a mechanism to control the shape of the Pöschl-Teller well and hence the intensity of the localized modes. Most importantly, our results reveal that even with a small fluctuation present in the trapping potential bearing dissipation, the system is robust enough to support stable propagation of nonlinear modes. •Generalized NLSE for BEC trapped in a PT-symmetric Pöschl-Teller potential.•The nonlinear stationary modes in terms of hypergeometric functions.•One-parameter family of potential using the isospectral Hamiltonian approach.•Effect of Riccati parameter on the intensity profile of matter-wave solitons.•Numerical stability and simulation of the localized modes in the PT symmetry regime.