title: Three-dimensional nonlinear lattices: from oblique vortices and octupoles to discrete diamonds and vortex cubes.
abstract: We construct a variety of novel localized topological structures in the 3D discrete nonlinear Schrödinger equation. The states can be created in Bose-Einstein condensates trapped in strong optical lattices and crystals built of microresonators. These new structures, most of which have no counterparts in lower dimensions, range from multipole patterns and diagonal vortices to vortex "cubes" (stack of two quasiplanar vortices) and "diamonds" (formed by two orthogonal vortices).
authors.affiliation: Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego California 92182-7720, USA.
authors.forename: R
authors.initials: R
authors.lastname: Carretero-González
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: B A
authors.initials: BA
authors.lastname: Malomed
authors.forename: D J
authors.initials: DJ
authors.lastname: Frantzeskakis