{"paper":{"title":"A new class of Traveling Solitons for cubic Fractional Nonlinear Schrodinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yannick Sire, Younghun Hong","submitted_at":"2015-01-07T09:41:59Z","abstract_excerpt":"We consider the one-dimensional cubic fractional nonlinear Schr\\\"odinger equation $$i\\partial_tu-(-\\Delta)^\\sigma u+|u|^{2}u=0,$$ where $\\sigma \\in (\\frac12,1)$ and the operator $(-\\Delta)^\\sigma$ is the fractional Laplacian of symbol $|\\xi|^{2\\sigma}$. Despite of lack of any Galilean-type invariance, we construct a new class of traveling soliton solutions of the form $$u(t,x)=e^{-it(|k|^{2\\sigma}-\\omega^{2\\sigma})}Q_{\\omega,k}(x-2t\\sigma|k|^{2\\sigma-2}k),\\quad k\\in\\mathbb{R},\\ \\omega>0$$ by a rather involved variational argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01415","kind":"arxiv","version":2},"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"}