THE LONGITUDINAL EXCITATION SPECTRUM OF AN ELONGATED BOSE-EINSTEIN CONDENSATE

In this manuscript we show an efficient numerical approach for the longitudinal excitation spectrum of a quasi-one-dimensional collisionally-inhomogeneous Bose-Einstein condensate. We obtain by variational means the nonlinear ordinary differential equations of a generic longitudinal excitation and determine numerically the onset of instability, to identify which excitation is most likely to be observed experimentally. To quantify the efficiency of our approach, we study a cigar-shaped condensate with weak collisionally-inhomogeneous two-body interactions and show that the position of the resonance observed in the longitudinal excitation spectrum is higher than that observed for a condensate with homogeneous two-body interactions.