{"paper":{"title":"Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS"],"primary_cat":"math.AP","authors_text":"Claudio Mu\\~noz, Michal Kowalczyk, Yvan Martel","submitted_at":"2019-03-29T12:01:47Z","abstract_excerpt":"We consider the dynamics of even solutions of the one-dimensional nonlinear Klein-Gordon equation $\\partial_t^2 \\phi - \\partial_x^2 \\phi + \\phi - |\\phi|^{2\\alpha} \\phi =0$ for $\\alpha>1$, in the vicinity of the unstable soliton $Q$. Our main result is that stability in the energy space $H^1(\\mathbb R)\\times L^2(\\mathbb R)$ implies asymptotic stability in a local energy norm. In particular, there exists a Lipschitz graph of initial data leading to stable and asymptotically stable trajectories.\n  The condition $\\alpha>1$ corresponds to cases where the linearized operator around $Q$ has no resona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12460","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"}