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We show that if the perturbation is compact and of bounded variation, then the initial value problem for the KdV equation has a classical solution. Our method is the inverse scattering transform method in the form of the Riemann-Hilbert problem method. Namely, we construct the corresponding spectral functions $a(\\lambda), r(\\lambda),$ and give characteri"},"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":"1901.07470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-01-22T17:10:19Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f3da2d147a29e3bcbae7d2a192160a3eb831c537d1d3afe1fc76563faecf7202","abstract_canon_sha256":"06d64dae9f8bef43c2926a5ea82fa3c86a2658f4dd47faf11b87dc9c748cebba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:44.702910Z","signature_b64":"zs106D0lGLn1qUiW8gDFsRqfebnFz0Gpft2oqw7FREaklSoZHXpofj6YZClA14Giox1geMpVRw5tfzyFQkK3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fb092a152725961d15b2c73e9dbff4bf9ef09e9fd1be81a88621e5ac432fdc0","last_reissued_at":"2026-05-17T23:55:44.702254Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:44.702254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a class of compact perturbations of the special pole-free joint solution of KdV and $P_I^2.$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Minakov, B. Dubrovin","submitted_at":"2019-01-22T17:10:19Z","abstract_excerpt":"We consider perturbations of the special pole-free joint solution $U(x,t)$ of the Korteweg--de Vries equation $u_t+uu_x+\\frac{1}{12}u_{xxx}=0$ and $P_I^2$ equation $u_{xxxx}+10u_x^2+20uu_{xx}+40(u^3-6tu+6x)=0$ under the action of the KdV flow. We show that if the perturbation is compact and of bounded variation, then the initial value problem for the KdV equation has a classical solution. Our method is the inverse scattering transform method in the form of the Riemann-Hilbert problem method. 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