{"paper":{"title":"Segregated Vector Solutions for linearly coupled Nonlinear Schr\\\"odinger Systems","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Shuangjie Peng","submitted_at":"2013-10-07T09:56:55Z","abstract_excerpt":"We consider the following system linearly coupled by nonlinear Schr\\\"odinger equations in $\\R^3$ $$ \\left\\{\\begin{array}{ll} -\\Delta u_j+u_j=u^3_j-\\va\\sum\\limits_{i\\neq j}^N u_i,\\{1cm}& x\\in \\R^3, \\{0.2cm}\\\\ u_j\\in H^1(\\R^3),\\quad j=1,\\cdots,N, \\end{array} \\right. $$ where $\\va\\in\\R$ is a coupling constant. This type of system arises in particular in models in nonlinear $N$-core fiber.\n  We examine the effect of the linear coupling to the solution structure. When $N=2,3$, for any prescribed integer $\\ell\\ge 2$, we construct a non-radial vector solutions of segregated type, with two components "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1718","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"}