{"paper":{"title":"Standing waves for coupled nonlinear Schrodinger equations with decaying potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenming Zou, Zhijie Chen","submitted_at":"2013-03-01T07:08:18Z","abstract_excerpt":"We study the following singularly perturbed problem for a coupled nonlinear Schr\\\"{o}dinger system: {displaymath} {cases}-\\e^2\\Delta u +a(x) u = \\mu_1 u^3+\\beta uv^2, \\quad x\\in \\R^3, -\\e^2\\Delta v +b(x) v =\\mu_2 v^3+\\beta vu^2, \\quad x\\in \\R^3, u> 0, v> 0 \\,\\,\\hbox{in $\\R^3$}, u(x), v(x)\\to 0 \\,\\,\\hbox{as $|x|\\to \\iy$}.{cases}{displaymath} Here, $a, b$ are nonnegative continuous potentials, and $\\mu_1,\\mu_2>0$. We consider the case where the coupling constant $\\beta>0$ is relatively large. Then for sufficiently small $\\e>0$, we obtain positive solutions of this system which concentrate around"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0099","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"}