Nonautonomous solitons of Bose-Einstein condensation in a linear potential with an arbitrary time-dependence

TL;DR

This paper develops a Hirota method to derive exact nonautonomous soliton solutions for Bose-Einstein condensates under a time-dependent linear potential, revealing effects on soliton velocity and elastic collisions.

Contribution

It introduces a novel analytical approach to solve the mean-field model with arbitrary time-dependent potentials, providing explicit nonautonomous soliton solutions.

Findings

Time-dependent potential influences NSS velocity.

Soliton collisions are elastic.

Velocity can increase or oscillate over time.

Abstract

In the presence of a linear potential with an arbitrary time-dependence, Hirota method is developed carefully for applying into the effective mean-field model of quasi-one-dimensional Bose-Einstein condensation with repulsive interaction. We obtain the exact nonautonomous soliton solution (NSS) analytically. These solutions show that the time-dependent potential can affect the velocity of NSS. In some special cases the velocity has the character of both increase and oscillation with time. A detail analysis for the asymptotic behaviour of solutions shows that the collision of two NSSs is elastic.