Modulation of breathers in cigar-shaped Bose–Einstein condensates

2009/12/31 by Wesley B. Cardoso, W. B. Cardoso, A. T. Avelar +1 · 2 citations
Physics and Astronomy · #Ansatz #Bose–Einstein condensate #Breather #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Mathematical physics #Modulation (music) #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear system #Perturbation (astronomy) #Physics #Quantum mechanics #Strong Light-Matter Interactions #cond-mat.quant-gas #quant-ph

paper · pdf · doi:10.1016/j.physleta.2010.04.050

published as Physics Letters A,374(2010)2640-2645

openalex publication_date 2010/04/23 · arxiv created 2010/05/23 · arxiv updated 2010/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Similarity transformations for nonlinear Schrödinger equations with time-dependent coefficients
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate
• Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions
• Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor
• Controlled Collapse of a Bose-Einstein Condensate
• Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
• Dynamics of Bose-Einstein condensates in optical lattices
• Fully Three Dimensional Breather Solitons Can Be Created Using Feshbach Resonances
• Breathers and Raman scattering in a two-leg ladder with staggered Dzyaloshinskii-Moriya interaction
• Bose-Einstein Condensation in a Gas of Sodium Atoms
• Stabilization and destabilization of second-order solitons against perturbations in the nonlinear Schrödinger equation
• From Feshbach-resonance managed Bose–Einstein condensates to anisotropic universes: Applications of the Ermakov–Pinney equation with time-dependent nonlinearity

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