# Study of implosion in an attractive Bose-Einstein condensate

## TL;DR

This paper investigates the collapse behavior of an attractive Bose-Einstein condensate using analytical and numerical solutions of the Gross-Pitaevskii equation, focusing on critical atom numbers and stability dynamics.

## Contribution

It provides a combined analytical and numerical analysis of implosion phenomena in attractive BECs, including a new calculation of the critical atom number using variational methods.

## Key findings

- Determined the critical atom number for stability.
- Analyzed collapse dynamics through numerical simulations.
- Validated analytical predictions with numerical results.

## Abstract

By solving the Gross-Pitaevskii equation analytically and numerically, we reexamine the implosion phenomena that occur beyond the critical value of the number of atoms of an attractive Bose-Einstein condensate (BEC) with cigar-shape trapping geometry. We theoretically calculate the critical number of atoms in the condensate by using Ritz's variational optimization technique and investigate the stability and collapse dynamics of the attractive BEC by numerically solving the time dependent Gross-Pitavskii equation.