Soliton response to transient trap variations

TL;DR

This paper investigates how bright and dark solitons respond to rapid, transient changes in an expulsive trap, providing exact solutions and revealing phenomena like rapid pulse amplification.

Contribution

It introduces a method to derive exact soliton solutions under transient trap variations using linear Schrödinger solutions combined with nonlinear equations.

Findings

Exact soliton profiles for transient trap variations

Identification of rapid pulse amplification scenarios

Analytical approach for time-dependent trapping potentials

Abstract

The response of bright and dark solitons to rapid variations in an expulsive longitudinal trap is investigated. We concentrate on the effect of transient changes in the trap frequency in the form of temporal delta kicks and the hyperbolic cotangent functions. Exact expressions are obtained for the soliton profiles. This is accomplished using the fact that a suitable linear Schrodinger stationary state solution in time can be effectively combined with the solutions of non-linear Schrodinger equation, for obtaining solutions of the Gross-Pitaevskii equation with time dependent scattering length in a harmonic trap. Interestingly, there is rapid pulse amplification in certain scenarios.