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We are interested in algebraic standing waves i.e standing waves with algebraic decay above equation in dimensions n (n = 1, 2, 3). We prove the instability of these solutions in the cases DDF (we use abbreviation D: defocusing (ai < 0), F:focusing (ai > 0)) and DFF when n = 2, 3 and in the case DFF with a1 = --1, a3 = 1 and a2 < 32/15$\\sqrt$6 when n = 1. Under these assumptions, the standing waves are orbitally unstable in the case of small positive frequency."},"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":"2110.07899","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-10-15T07:29:03Z","cross_cats_sorted":[],"title_canon_sha256":"d705a83ba45a1ff78622d1680055542a8da8fd5fac72b347e7f1366257dbedf5","abstract_canon_sha256":"e2bba7653b245c119306c72fd283546089981eeb6ddfef2c75bfd247242e12c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:07:05.829538Z","signature_b64":"De6b0RsHNPCGym1THC05ktZHaEjUIJTmIyRNEMRwoAeB7Atpa4LOdU5vUG+NqVt7KRuOSX7fDRyHinxfww0hAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc8b23bd6c1c8deedc33d45dcb97d522e9bbe190faefefc797ac2463eb8c6c9c","last_reissued_at":"2026-07-05T04:07:05.829139Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:07:05.829139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Instability of algebraic standing waves for nonlinear Schr\\''odinger equations with triple power nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Phan van Tin (IMT, UT3)","submitted_at":"2021-10-15T07:29:03Z","abstract_excerpt":"We consider the following triple power nonlinear Schr{\\\"o}dinger equation: iut + $\\Delta$u + a 1 |u|u + a 2 |u| 2 u + a 3 |u| 3 u = 0. We are interested in algebraic standing waves i.e standing waves with algebraic decay above equation in dimensions n (n = 1, 2, 3). We prove the instability of these solutions in the cases DDF (we use abbreviation D: defocusing (ai < 0), F:focusing (ai > 0)) and DFF when n = 2, 3 and in the case DFF with a1 = --1, a3 = 1 and a2 < 32/15$\\sqrt$6 when n = 1. 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