Abstract
The present chapter deals with a time-dependent inhomogeneous cubic nonlinear Schrodinger equation with external real/complex potential which at ultralow temperatures, describes the time-dependent wavefunction of the Bose–Einstein condensates when only the two-body interatomic interactions are taken into account. Through the analytical investigation of this equation, we investigate (i) the generation of matter-wave solitons of BECs with time-dependent atomic scattering length in an expulsive parabolic potential, (ii) the dynamics of BECs with feeding/loss of atoms, (iii) the interaction of matter-wave solitons in BECs with time-dependent scattering length and varying potentials, and (iv) the nonautonomous matter waves in 1D BECs.
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