Construction of exact solutions by spatial translations in inhomogeneous nonlinear Schrödinger equations

2001/06/23 by Juan José García‐Ripoll, Juan J. Garcia-Ripoll, Víctor M. Pérez‐García +3 · 2 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Nonlinear Photonic Systems #Strong Light-Matter Interactions #cond-mat.soft #nlin.PS

paper · pdf · doi:10.1103/physreve.64.056602

published as Phys. Rev. E 64, 056602 (2001) · Submitted to Phys. Rev

arxiv created 2001/06/23 · openalex publication_date 2001/10/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a general nonlinear Schrödinger equation with a time-dependent harmonic potential. Despite the lack of translational invariance, we find a symmetry transformation that, up from any solution, produces infinitely many others that are centered on classical trajectories. The results presented here imply that, not only the center of mass of the wave packet satisfies the Ehrenfest theorem and is decoupled from the dynamics of the wave packet, but also the shape of the solution is independent of the behavior of the center of the wave. Our findings have implications on the dynamics of Bose-Einstein condensates in magnetic traps.

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• Fractional Schrödinger dynamics and decoherence
• A Model for Conservative Chaos Constructed from Multicomponent Bose–Einstein Condensates with a Trap in Two Dimensions

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