Bright-matter solitons in a uniformly feeded Bose–Einstein condensate with expulsive harmonic potential

The Gross–Pitaevskii equation, which describes the dynamics of a one-dimensional uniformly feeded attractive Bose–Einstein condensate in an expulsive potential of arbitrary harmonic shape − a 2 x 2 + a 1 x , is solved analytically following the inverse scattering transform method. Within this approach, bright-matter waves are obtained as exact envelope-soliton solutions of the nonlinear Schrödinger equation with a complex harmonic potential. The envelope shapes mimic double-lump pulses of unequal amplitudes symmetric with respect to the potential maximum, moving simultaneously at nonconstant accelerations with amplitudes that vary in time.