{"paper":{"title":"Modulational and Parametric Instabilities of the Discrete Nonlinear Schr\\\"odinger Equation","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"A.R. Bishop, A. Smerzi, P.G. Kevrekidis, Z. Rapti","submitted_at":"2004-04-25T01:18:35Z","abstract_excerpt":"We examine the modulational and parametric instabilities arising in a non-autonomous, discrete nonlinear Schr{\\\"o}dinger equation setting. The principal motivation for our study stems from the dynamics of Bose-Einstein condensates trapped in a deep optical lattice. We find that under periodic variations of the heights of the interwell barriers (or equivalently of the scattering length), additionally to the modulational instability, a window of parametric instability becomes available to the system. We explore this instability through multiple-scale analysis and identify it numerically. Its pri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0404600","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"}