{"paper":{"title":"Three-Dimensional Nonlinear Lattices: From Oblique Vortices and Octupoles to Discrete Diamonds and Vortex Cubes","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"B.A. Malomed, D.J. Frantzeskakis, P.G. Kevrekidis, R. Carretero-Gonzalez","submitted_at":"2005-01-27T18:40:17Z","abstract_excerpt":"We construct a variety of novel localized states with distinct topological structures in the 3D discrete nonlinear Schr{\\\"{o}}dinger 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 purely real patterns of dipole, quadrupole and octupole types to vortex solutions, such as \"diagonal\" and \"oblique\" vortices, with axes oriented along the respective directions $(1,1,1)$ and $(1,1,0)$. Vortex \"cubes\" (stacks of two quasi-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0501680","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}