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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.0099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-01T07:08:18Z","cross_cats_sorted":[],"title_canon_sha256":"810519ed551d0c337d9a2b4e37e4ef27348a05b84c8919b65bc1a20d9d4c655e","abstract_canon_sha256":"94e318240db6372db825a91d6daa5338b4dad300b70fcef8cd3d04b41a2457d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:25.657955Z","signature_b64":"gZK6+zzLttRgNKb2uelwjz0Ax8dP9vZSdM/u5IN++CuTWcfJYJtu4XuEch3z88bzWj8gqgTYAWGdOfxDd77fBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ff534a6e035e2d53da5ff67728db10df5434e070893fb665da2b3f0f12fa983","last_reissued_at":"2026-05-18T01:51:25.657228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:25.657228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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