{"paper":{"title":"Existence and stability of standing waves for coupled nonlinear Hartree type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Santosh Bhattarai","submitted_at":"2019-02-07T14:01:44Z","abstract_excerpt":"We study existence and stability of standing waves for coupled nonlinear Hartree type equations \\[ -i\\frac{\\partial}{\\partial t}\\psi_j=\\Delta \\psi_j+\\sum_{k=1}^m \\left(W\\star |\\psi_k|^p \\right)|\\psi_j|^{p-2}\\psi_j, \\] where $\\psi_j:\\mathbb{R}^N\\times \\mathbb{R}\\to \\mathbb{C}$ for $j=1, \\ldots, m$ and the potential $W:\\mathbb{R}\\to [0, \\infty)$ satisfies certain assumptions. Our method relies on a variational characterization of standing waves based on minimization of the energy when $L^2$ norms of component waves are prescribed. We obtain existence and stability results for two and three-compo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02618","kind":"arxiv","version":1},"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"}