Dynamics of bright matter wave solitons in Bose–Einstein condensates in an expulsive parabolic and complex potential

Abstract

We present a new family of analytic solutions of the nonlinear Schrödinger equation with an imaginary potential that describes the dynamics of a bright soliton in a Bose-Einstein condensate with an expulsive parabolic and complex potential. We found that under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the value of the feeding parameter.

Compensation process and generation of chirped femtosecond solitons and double-kink solitons in Bose–Einstein condensates with time-dependent atomic scattering length in a time-varying complex potential

“…2 of a BEC with the increasing of the absolute value of the s-wave scattering length (with loss of atoms) has an increase (decrease) in the peak value; also, the density |ψ(x, t)| 2 of a BEC with the decreasing of the absolute value of the s-wave scattering length (with feeding of atoms) has a decrease (increase) in the peak value [13,15]. We thus conclude that Eq.…”

“…Because |α| << 1, parameter α expresses the trapping frequency in the x− direction [14]. γ is a small parameter related to the feeding (γ > 0) or loss (γ < 0) of atoms in the condensate resulting from the contact with the thermal cloud and three-body recombination [15,16]. In this study, the s-wave scattering length is allowed to be a function of time t [17] so that parameter g of the nonlinearity and strength α of the magnetic trap are be time-dependent; also, parameter γ of the gain/loss of atoms is assumed to be time-dependent.…”

Stability of exact solutions of the cubic-quintic nonlinear Schrödinger equation with periodic potential

“…As in BECs with two-body interaction [21][22][23], the proper choice of the potential allows one to construct a large class of exact solutions. The external potential considered in this work is a generalization of the sinusoidal potential (standing light wave potential) [24]:…”

Modulational Instability and Exact Soliton and Periodic Solutions for Two Weakly Coupled Effectively 1d Condensates Trapped in a Double-Well Potential

“…[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] The experimental observation of dark 21,22 and bright 23,24 solitons in a BEC has drawn attention to various aspects of the dynamics of nonlinear matter waves, such as vortex dynamics, 25 soliton propagation, 26 interference patterns, 27 and modulational instability (MI). At zero temperature such a system is supposed to be fully condensed and is described by the mean-field Gross-Pitaevskii (GP) equation.…”