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Our main aim is to study the large-$t$ behavior of the solution of this problem. We show that for $R\\in\\left(\\frac{(2n-1)\\pi}{2A},\\frac{(2n+1)\\pi}{2A}\\right)$, $n=1,2,\\dots$, the $(x,t)$ plane splits into\n  $4n+2$ sectors exhibiting different asymptotic beh"},"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":"1908.06415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T10:03:30Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"870273455e72a467d386109864128e501f2162f63eeddb933d07cc17849f1a75","abstract_canon_sha256":"342450632b023222fce4dc1679feb62100d9dff0274bc21c6a568685a56ab911"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:50:37.240599Z","signature_b64":"VOjaMHOLdtV/c3mqb4Y1DNCfaCYEFIOOFaAave1HNYwwiD4DMCx8BoS3ANgabVfYf/XarHGp/b3rVA66CmShDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6869095b09c7f51c52737ea3da31865c8b5f5d4132fb9dd9e3b08637dc93c7b","last_reissued_at":"2026-07-05T02:50:37.240029Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:50:37.240029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long-time asymptotics for the integrable nonlocal focusing nonlinear Schr\\\"odinger equation for a family of step-like initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.AP","authors_text":"Dmitry Shepelsky, Yan Rybalko","submitted_at":"2019-08-18T10:03:30Z","abstract_excerpt":"We study the Cauchy problem for the integrable nonlocal focusing nonlinear Schr\\\"odinger (NNLS) equation $\niq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\\bar{q}(-x,t)=0 $\nwith the step-like initial data close to the ``shifted step function'' $\\chi_R(x)=AH(x-R)$, where $H(x)$ is the Heaviside step function, and $A>0$ and $R>0$ are arbitrary constants. Our main aim is to study the large-$t$ behavior of the solution of this problem. 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