{"paper":{"title":"Energy preserving methods for nonlinear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.optics","quant-ph"],"primary_cat":"math.NA","authors_text":"Christophe Besse (IMT), Guillaume Dujardin (MEPHYSTO-POST), Ingrid Lacroix-Violet (RAPSODI ), Stephane Descombes (NACHOS)","submitted_at":"2018-12-12T10:57:01Z","abstract_excerpt":"This paper is concerned with the numerical integration in time of nonlinear Schr\\\"odinger equations using different methods preserving the energy or a discrete analog of it. The Crank-Nicolson method is a well known method of order 2 but is fully implicit and one may prefer a linearly implicit method like the relaxation method introduced in [10] for the cubic nonlinear Schr{\\\"o}dinger equation. This method is also an energy preserving method and numerical simulations have shown that its order is 2. In this paper we give a rigorous proof of the order of this relaxation method and propose a gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04890","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"}