{"paper":{"title":"Well-posedness, energy and charge conservation for nonlinear wave equations in discrete space-time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NA"],"primary_cat":"math.AP","authors_text":"Alexander Komech, Andrew Comech","submitted_at":"2010-08-18T06:56:25Z","abstract_excerpt":"We consider the problem of discretization for the U(1)-invariant nonlinear wave equations in any dimension. We show that the classical finite-difference scheme used by Strauss and Vazquez \\cite{MR0503140} conserves the positive-definite discrete analog of the energy if the grid ratio is $dt/dx\\le 1/\\sqrt{n}$, where $dt$ and $dx$ are the mesh sizes of the time and space variables and $n$ is the spatial dimension. We also show that if the grid ratio is $dt/dx=1/\\sqrt{n}$, then there is the discrete analog of the charge which is conserved.\n  We prove the existence and uniqueness of solutions to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3032","kind":"arxiv","version":3},"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"}