Modulation of breathers in cigar-shaped Bose-Einstein condensates

TL;DR

This paper introduces a method to manipulate breather solutions in cigar-shaped Bose-Einstein condensates by transforming the nonautonomous Gross-Pitaevskii equation into an autonomous form, enabling stable localized oscillating states.

Contribution

It provides an analytical approach to modulate breathers in Bose-Einstein condensates via a transformation of the governing equations, supported by numerical stability analysis.

Findings

Successfully transforms nonautonomous to autonomous equations

Produces localized breather solutions with oscillating behavior

Demonstrates stability of solutions against perturbations

Abstract

We present new solutions to the nonautonomous nonlinear Schroedinger equation that may be realized through convenient manipulation of Bose-Einstein condensates. The procedure is based on the modulation of breathers through an analytical study of the one-dimensional Gross-Pitaevskii equation, which is known to offer a good theoretical model to describe quasi-one-dimensional cigar-shaped condensates. Using a specific Ansatz, we transform the nonautonomous nonlinear equation into an autonomous one, which engenders composed states corresponding to solutions localized in space, with an oscillating behavior in time. Numerical simulations confirm stability of the breathers against random perturbation on the input profile of the solutions.