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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.01415","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T09:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"805c71dab2c39c8e834d33995ff314dabca1d915998ab7fc19fcf2d5c6517fb7","abstract_canon_sha256":"b49d8ccde872c68e60e769790a94f607ac2853e67a591177c0dcde38b2b5fe15"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:16.216021Z","signature_b64":"IH8M/2RncBcIcsMnhrxZ0AVcsyFVo+scB1n7YyqCMolRg0unrlywEM4v2km8VIWeQOGpojmXoiIrpiAeZvo5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92c25dc6e74ed558420ef56eee2d2c6888fd63ac36bb462e41840d4871c6f485","last_reissued_at":"2026-05-18T01:33:16.215280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:16.215280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $|\\xi|^{2\\sigma}$. 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