{"paper":{"title":"Ill-Posedness of the Third Order NLS Equation with Raman Scattering Term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nobu Kishimoto, Yoshio Tsutsumi","submitted_at":"2017-06-28T03:07:14Z","abstract_excerpt":"We consider the ill-posedness and well-posedness of the Cauchy problem for the third order NLS equation with Raman scattering term on the one dimensional torus. It is regarded as a mathematical model for the photonic crystal fiber oscillator. Regarding the ill-posedness, we show the nonexistence of solutions in the Sobolev space and the norm inflation of the data-solution map under slightly different conditions, respectively. We also prove the local unique existence of solutions in the analytic function space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09111","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"}