{"paper":{"title":"Dynamics of breathers in the Gardner hierarchy: universality of the variational characterization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS","nlin.SI"],"primary_cat":"math.AP","authors_text":"Eleomar Cardoso, Miguel A. Alejo","submitted_at":"2019-01-29T17:26:54Z","abstract_excerpt":"We present a new variational characterization of breather solutions of any equation of the \\emph{focusing} Gardner hierarchy. This hierarchy is characterized by a nonnegative index $n$, and $2n+1$ represents the order of the corresponding PDE member. In this paper, we first show the existence of such breathers, and that they are solutions of the (2n+1)th-order Gardner equation. Then we prove a \\emph{variational universality property}, in the sense that all these breather solutions satisfy the \\emph{same} fourth order stationary elliptic ODE, regardless the order of the hierarchy member. This f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10409","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"}