{"paper":{"title":"On the Schr\\\"odinger equations with isotropic and anisotropic fourth-order dispersion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Banquet, Elder J. Villamizar-Roa","submitted_at":"2014-02-10T16:05:26Z","abstract_excerpt":"This paper deals with the Cauchy problem associated to the nonlinear fourth-order Schr\\\"odinger equation with isotropic and anisotropic mixed dispersion. This model is given by the equation $i\\partial _{t}u+\\epsilon \\Delta u+\\delta A u+\\lambda|u|^\\alpha u=0,$ $x\\in \\mathbb{R}^{n},$ $t\\in \\mathbb{R},$ where $A$ represents either the operator $\\Delta^2$ (isotropic dispersion) or $\\sum_{i=1}^d\\partial_{x_ix_ix_ix_i},\\ 1\\leq d<n$ (anisotropic dispersion), and $\\alpha, \\epsilon, \\lambda$ are given real parameters. We obtain local and global well-posedness results in spaces of initial data with low "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2193","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"}