Analytical three-dimensional bright solitons and soliton-pairs in Bose-Einstein condensates with time-space modulation

We provide analytical three-dimensional bright multi-soliton solutions to the (3+1)-dimensional Gross-Pitaevskii (GP) equation with time and space-dependent potential, time-dependent nonlinearity, and gain/loss. The zigzag propagation trace and the breathing behavior of solitons are observed. Different shapes of bright solitons and fascinating interactions between two solitons can be achieved with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.

💡 Research Summary

This paper presents exact analytical three‑dimensional (3D) bright soliton and multi‑soliton solutions of the (3+1)‑dimensional Gross‑Pitaevskii (GP) equation that incorporates a time‑ and space‑dependent external potential, a time‑varying nonlinear interaction coefficient, and a gain/loss term. The authors start by formulating the generalized GP equation

\