{"paper":{"title":"On the continuum limit for discrete NLS with long-range lattice interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Gigliola Staffilani, Kay Kirkpatrick","submitted_at":"2011-08-31T07:08:22Z","abstract_excerpt":"We consider a general class of discrete nonlinear Schroedinger equations (DNLS) on the lattice $h \\mathbb{Z}$ with mesh size $h>0$. In the continuum limit when $h \\to 0$, we prove that the limiting dynamics are given by a nonlinear Schroedinger equation (NLS) on $\\mathbb{R}$ with the fractional Laplacian $(-\\Delta)^\\alpha$ as dispersive symbol. In particular, we obtain that fractional powers $1/2 < \\alpha < 1$ arise from long-range lattice interactions when passing to the continuum limit, whereas NLS with the non-fractional Laplacian $-\\Delta$ describes the dispersion in the continuum limit fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6136","kind":"arxiv","version":2},"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"}