{"paper":{"title":"2D solutions of the hyperbolic discrete nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"J. D'Ambroise, P. G. Kevrekidis","submitted_at":"2018-10-01T14:09:59Z","abstract_excerpt":"We derive stationary solutions to the two-dimensional hyperbolic discrete nonlinear Schr\\\"odinger (HDNLS) equation by starting from the anti-continuum limit and extending solutions to include nearest-neighbor interactions in the coupling parameter. We use pseudo-arclength continuation to capture the relevant branches of solutions and explore their corresponding stability and dynamical properties (i.e., their fate when unstable). We focus on nine primary types of solutions: single site, double site in- and out-of-phase, squares with four sites in-phase and out-of phase in each of the vertical a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00712","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"}