{"paper":{"title":"Existence and orbital stability of standing waves for nonlinear Schr\\\"odinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Louis Jeanjean, Tianxiang Gou","submitted_at":"2015-12-30T14:31:34Z","abstract_excerpt":"In this paper we investigate the existence of solutions in $H^1(R^N) \\times H^1(R^N)$ for nonlinear Schr\\\"odinger systems of the form \\[ \\left\\{ \\begin{aligned} -\\Delta u_1 &= \\lambda_1 u_1 + \\mu_1 |u_1|^{p_1 -2}u_1 + r_1\\beta |u_1|^{r_1-2}u_1|u_2|^{r_2}, \\\\ -\\Delta u_2 &= \\lambda_2 u_2 + \\mu_2 |u_2|^{p_2 -2}u_2 + r_2 \\beta |u_1|^{r_1}|u_2|^{r_2 -2}u_2, \\end{aligned} \\right. \\] under the constraints \\[\\int_{R^N}|u_1|^2 \\, dx = a_1>0,\\quad \\int_{R^N}|u_2|^2 \\, dx = a_2>0. \\] Here $ N \\geq 1, \\beta >0, \\mu_i >0, r_i >1, 2 <p_i < 2 + \\frac{4}{N}$ for $i=1,2$ and $ r_1 + r_2 < 2 + \\frac{4}{N}$. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08952","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"}