{"paper":{"title":"Effective dynamics for $N$-solitons of the Gross-Pitaevskii equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","nlin.PS"],"primary_cat":"math.AP","authors_text":"Trevor Potter","submitted_at":"2010-09-24T18:29:32Z","abstract_excerpt":"We consider several solitons moving in a slowly varying external field. We show that the effective dynamics obtained by restricting the full Hamiltonian to the finite dimensional manifold of $ N$-solitons (constructed when no external field is present) provides a remarkably good approximation to the actual soliton dynamics. That is quantified as an error of size $ h^2 $ where $ h $ is the parameter describing the slowly varying nature of the potential. This also indicates that previous mathematical results of Holmer-Zworski for one soliton are optimal. For potentials with unstable equilibria t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4910","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"}