{"paper":{"title":"Solitary waves and $N$-particle algorithms for a class of Euler-Poincar\\'e equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dongyang Kuang, Long Lee, Roberto Camassa","submitted_at":"2014-04-18T19:01:57Z","abstract_excerpt":"We study a class of partial differential equations (PDEs) in the family of the so-called Euler-Poincar\\'e differential systems, with the aim of developing a foundation for numerical algorithms of their solutions. This requires particular attention to the mathematical properties of this system when the associated class of elliptic operators possesses non-smooth kernels. By casting the system in its Lagrangian (or characteristics) form, we first formulate a particles system algorithm in free space with homogeneous Dirichlet boundary conditions for the evolving fields. We next examine the deforma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4858","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"}