Dynamics of analytical three-dimensional solutions in Bose-Einstein condensates with time-dependent gain and potential

Abstract

Using the F-expansion method we systematically present exact solutions of the three-dimensional nonlinear generalized Gross-Pitaevskii equation, with time-varying gain or loss, in both attractive and expulsive harmonic confinement regimes. This approach allows us to obtain solitons for a large variety of solutions depending on the time-varying potential and the gain or loss profiles. The dynamics of these matter waves, including quasibreathing solitons, double-quasibreathing solitons, and three-quasibreathing solitons, is discussed. The explicit functions that describe the evolution of the amplitude, width, and trajectory of the soliton's wave center are presented exactly. It is demonstrated that an arbitrary additional time-dependent gain function can be added to the model to control the amplitude and width of the soliton and the nonlinearity without affecting the motion of the solitons' wave center. Additionally, a number of exact traveling waves, including the Faraday pattern formation, have been found. The obtained results may raise the possibility of relative experiments and potential applications.

Symbolic-computation study of bright solitons in the optical waveguides and Bose-Einstein condensates

“…For example, an amplified soliton, which is created due to the gain effect to increase the soliton energy [27,30], and the focusing effect caused by the resonant interaction [29], corresponds to the high local-matter density in the optical waveguides and BECs [29]. On account of the time-varying gain or loss from the thermal cloud [32,33], the propagation properties and management of the bright solitons in the optical waveguide and BEC can be described by the following (3+1)-dimensional Gross-Pitaevskii (GP) system with the time-varying control parameters [34][35][36][37][38][39]:…”

Bell‐Polynomial Approach and Integrability for the Coupled Gross–Pitaevskii Equations in Bose–Einstein Condensates

“…Work in connection with the dynamics of nonlinear matter‐wave solitons in the BECs has been done, such as the spontaneous symmetry breaking , symbiotic solitons , vortex dynamics , interference patterns , domain walls , and four‐wave mixing . Solitons in the BECs have been studied with time‐varying parameters, including the time‐dependent atomic wave scattering lengths which can be influenced by the Feshbach resonance, time‐varying gain or loss from the thermal cloud, and effects of variables diffraction .…”