Soliton solutions of 3D Gross-Pitaevskii equation by a potential control method
Renato Fedele, Bengt Eliasson, Fernando Haas, Padma Kant Shukla, Dusan, Jovanovic, Sergio De Nicola
TL;DR
This paper derives 3D soliton solutions for the Gross-Pitaevskii equation using a potential control method, enabling precise manipulation of Bose-Einstein condensates' localized states.
Contribution
It introduces a novel potential control approach to generate and stabilize 3D soliton solutions in Bose-Einstein condensates.
Findings
Analytic 3D soliton solutions derived
Numerical stability analysis confirms solution robustness
Potential design guides experimental control of BECs
Abstract
We present a class of three-dimensional solitary waves solutions of the Gross-Pitaevskii (GP) equation, which governs the dynamics of Bose-Einstein condensates (BECs). By imposing an external controlling potential, a desired time-dependent shape of the localized BEC excitation is obtained. The stability of some obtained localized solutions is checked by solving the time-dependent GP equation numerically with analytic solutions as initial conditions. The analytic solutions can be used to design external potentials to control the localized BECs in experiment.
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