Soliton dynamics and interaction in the Bose–Einstein condensates with harmonic trapping potential and time-varying interatomic interaction

Abstract

Investigated in this paper is the quasi-onedimensional Gross-Pitaevskii equation, which describes the dynamics of the Bose-Einstein condensates with the harmonic trapping potential and timevarying interatomic interaction. Via the Horita method and symbolic computation, analytic bright N-soliton solution is obtained. One-, two-and three-soliton solutions are analyzed graphically. Based on the limit analysis on the one-and two-soliton solutions, the modulation on the speed of the matter-wave bright solitons is realized. Via the parameters, the interaction between the matter-wave solitons are adjustable. Furthermore, an approach to construct the interference between the matter-wave solitons has been proposed. Finally, investigation on the three-soliton solution verifies our conclusions drawn from the one and two solitons. Our conclusions might be useful in the fields of the control on the matter-wave solitons, atom lasers, and atomic accelerators.

On multi-hump solutions of reverse space-time nonlocal nonlinear Schrödinger equation

“…The interference pattern becomes more prominent as we increase relative velocity. This interference pattern is due to the feedback of the wave properties of the soliton that take over at higher relative speeds [16][17][18]. Here these humps are nonlocally induced by coupling the two soliton solutions of reverse space-time nonlocal NLS equation at different but opposite sites.…”

“…But what is happening in the region where humps interact, is still debatable and will help us to explore many exciting features of nonlinear collisions. A few years back in 2016, Zhao et al studied nonlinear interference patterns associated with solitons asymptotically through density calculation and found that the pattern is contingent on relative velocities of the interacting solitons [16] (Also see [17,18]). Wave-like properties of soliton are intensively explored lately in the context of matter-wave in Bose-Einstein condensations [19][20][21].…”

Dynamics and stability of matter‐wave solitons in cigar‐shaped Bose–Einstein condensates dragged by Pöschl–Teller potential

“…Dynamics and stability of solitons have been investigated both theoretically and experimentally in BECs confined by magnetic traps (harmonic potentials) [8, 9], optical lattices (periodic potentials) [10] and double‐well potentials [11]. Recently, BECs trapped by the symmetrical Pöschl–Teller (PT) potential (hyperbolic potential) have been theoretically studied [12].…”