Modulational instability and bright solitary wave solution for Bose-Einstein condensates with time-dependent scattering length and harmonic potential

Abstract

We consider the one-dimensional Gross-Pitaevskii (GP) equation, which governs the dynamics of Bose-Einstein condensate (BEC) matter waves with time-dependent scattering length and a harmonic trapping potential. We present the integrable condition for the one-dimensional GP equation and obtain the exact analytical solution which describes the modulational instability and the propagation of a bright solitary wave on a continuous wave (cw) background. Moreover, by employing the adiabatic perturbation theory for a bright soliton, we obtain approximative bright solitary wave solutions under near-integrable conditions. Both the exact and approximative solutions show that the amplitude of a bright solitary wave with zero boundary condition depends on the scattering length while its motion depends on the external trapping potential. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.