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Mathematics and Computers in Simulation 69 (2005) 537–552 Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates G. Theocharis a , D.J. Frantzeskakis a , P.G. Kevrekidis b , R. Carretero-Gonz ´ alez c, , B.A. Malomed d a  Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece b  Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA c  Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, USA d  Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel A vailable online 6 July 2005 Abstract We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose–Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with the optical lattice period being smaller, larger, or comparable to the width of the dark soliton. Analytical results, based on perturbation techniques, for the motion of the dark soliton are obtained and compared to direct numerical simulations. Radiation effects are also considered. Finally, we demonstrate that a moving optical lattice may capture and drag a dark soliton. © 2005 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Soliton; Matter waves; Optical lattice; Bose–Einstein condensation 1. Introduction Dark solitons (DSs), the most fundamental nonlinear excitations of the nonlinear Schr ¨ odinger (NLS) equa tion with a defocusing nonl inea rity , have been widely stud ied in man y bran ches of Physics. Corresponding author. Tel.: +1 619 594 7252; fax: +1 619 594 2029.  E-mail address: [email protected]. edu (R. Carretero-Gonz´ alez). URL: http://nlds.sdsu.edu/. 0378-475 4/$30.00 © 2005 IMACS. Published by Elsevier B.V . All rights reserved. doi:10.1016/j.matcom.2005.03.017

G. Theocharis et al- Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates

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