Robust Vortex Lines, Vortex Rings and Hopfions in Three-Dimensional Bose-Einstein Condensates

R. N. Bisset,1,* Wenlong Wang,2 C. Ticknor,3 R. Carretero-González,4 D. J. Frantzeskakis,5 L. A. Collins,3 and P. G. Kevrekidis1,6 1Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 2Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA 3Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 4Nonlinear Dynamical Systems Group,† Computational Sciences Research Center, and Department of Mathematics and Statistics, San Diego State University, San Diego, California 92182-7720, USA 5Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece 6Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA (Received 15 October 2015; published 7 December 2015)