Matter-wave solitons with a periodic, piecewise-constant scattering length

A. S. Rodrigues, P. G. Kevrekidis, Mason A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop
Phys. Rev. A 78, 013611 – Published 8 July 2008

Abstract

Motivated by recent proposals of “collisionally inhomogeneous” Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons of a BEC characterized by a periodic, piecewise-constant scattering length. We use a “stitching” approach to analytically approximate the pertinent solutions of the underlying nonlinear Schrödinger equation by matching the wave function and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that stationary solitons must be centered in one of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations.

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  • Received 6 December 2007

DOI:https://doi.org/10.1103/PhysRevA.78.013611

©2008 American Physical Society

Authors & Affiliations

A. S. Rodrigues1, P. G. Kevrekidis2, Mason A. Porter3, D. J. Frantzeskakis4, P. Schmelcher5,6, and A. R. Bishop7

  • 1Departamento de Física/CFP, Faculdade de Ciências, Universidade do Porto, R. Campo Alegre, 687–4169-007 Porto, Portugal
  • 2Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
  • 3Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford, OX1 3LB, United Kingdom
  • 4Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84, Greece
  • 5Theoretische Chemie, Physikalisch-Chemisches Institut, Im Neuenheimer Feld 229, Universität Heidelberg, 69120 Heidelberg, Germany
  • 6Physikalisches Institut, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany
  • 7Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Issue

Vol. 78, Iss. 1 — July 2008

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