{"paper":{"title":"Orbitally stable standing waves of a mixed dispersion nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Denis Bonheure, Ederson Moreira dos Santos, Jean-Baptiste Cast\\'eras, Robson Nascimento","submitted_at":"2017-10-26T15:56:25Z","abstract_excerpt":"We study the mixed dispersion fourth order nonlinear Schr\\\"odinger equation \\begin{equation*} %\\tag{\\protect{4NLS}}\\label{4nls} i \\partial_t \\psi -\\gamma \\Delta^2 \\psi +\\beta \\Delta \\psi +|\\psi|^{2\\sigma} \\psi =0\\ \\text{in}\\ \\R \\times\\R^N, \\end{equation*} where $\\gamma,\\sigma>0$ and $\\beta \\in \\R$. We focus on standing wave solutions, namely solutions of the form $\\psi (x,t)=e^{i\\alpha t}u(x)$, for some $\\alpha \\in \\R$. This ansatz yields the fourth-order elliptic equation \\begin{equation*} %\\tag{\\protect{*}}\\label{4nlsstar} \\gamma \\Delta^2 u -\\beta \\Delta u +\\alpha u =|u|^{2\\sigma} u. \\end{eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09775","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"}