Abstract
Motivated by recent experimental investigations in the context of matter wave solitons in Bose-Einstein condensates (BECs), we consider the 1+1 Gross-Pitaevskii equation with complex time-varying harmonic potential, and time-varying cubic and quintic nonlinearities. By performing a modified lens-type transformation for the one-dimensional GP equation, we present one and/or two parameter exact analytical solutions which describe the propagation of bright, kink, and dark solitary waves on the vanishing continuous wave (cw) background. Based on exact analytical solutions of the GP equation, we investigate analytically the dynamics of matter-wave solitons in the BEC systems. Our studies show that the solitons’ amplitude depends on both the scattering length and the feeding/loss term of the potential while their motion depends on the external trapping potential and solution parameters.
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