{"paper":{"title":"On $W_{1+\\infty}$ 3-algebra and integrable system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Ke Wu, Min-Ru Chen, Shi-Kun Wang, Wei-Zhong Zhao, Xiao-Li Wang","submitted_at":"2013-09-18T12:37:53Z","abstract_excerpt":"We construct the $W_{1+\\infty}$ 3-algebra and investigate the relation between this infinite-dimensional 3-algebra and the integrable systems. Since the $W_{1+\\infty}$ 3-algebra with a fixed generator $W^0_0$ in the operator Nambu 3-bracket recovers the $W_{1+\\infty}$ algebra, it is natural to derive the KP hierarchy from the Nambu-Poisson evolution equation. For the general case of the $W_{1+\\infty}$ 3-algebra, we directly derive the KP and KdV equations from the Nambu-Poisson evolution equation with the different Hamiltonian pairs. We also discuss the connection between the $W_{1+\\infty}$ 3-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4627","kind":"arxiv","version":4},"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"}