{"paper":{"title":"Orbital stability of periodic waves in the class of reduced Ostrovsky equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.PS","nlin.SI"],"primary_cat":"math.AP","authors_text":"Dmitry E. Pelinovsky, Edward R. Johnson","submitted_at":"2016-03-09T16:50:06Z","abstract_excerpt":"Periodic travelling waves are considered in the class of reduced Ostrovsky equations that describe low-frequency internal waves in the presence of rotation. The reduced Ostrovsky equations with either quadratic or cubic nonlinearities can be transformed to integrable equations of the Klein--Gordon type by means of a change of coordinates. By using the conserved momentum and energy as well as an additional conserved quantity due to integrability, we prove that small-amplitude periodic waves are orbitally stable with respect to subharmonic perturbations, with period equal to an integer multiple "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02961","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":""},"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"}