{"paper":{"title":"Solitary Waves and Compactons in a class of Generalized Korteweg-DeVries Equations","license":"","headline":"","cross_cats":["nlin.PS"],"primary_cat":"patt-sol","authors_text":"Fred Cooper (LANL, Harvey Shepard (UNH), Pasquale Sodano (U. Perugia), UNH)","submitted_at":"1993-05-18T15:36:27Z","abstract_excerpt":"We study the class of generalized Korteweg-DeVries equations derivable from the Lagrangian: $ L(l,p) = \\int \\left( \\frac{1}{2} \\vp_{x} \\vp_{t} - { {(\\vp_{x})^{l}} \\over {l(l-1)}} + \\alpha(\\vp_{x})^{p} (\\vp_{xx})^{2} \\right) dx, $ where the usual fields $u(x,t)$ of the generalized KdV equation are defined by $u(x,t) = \\vp_{x}(x,t)$. This class contains compactons, which are solitary waves with compact support, and when $l=p+2$, these solutions have the feature that their width is independent of the amplitude. We consider the Hamiltonian structure and integrability properties of this class of Kd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"patt-sol/9305006","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/patt-sol/9305006/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}