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The main aim is to study the long-time behavior of the solution of this problem. We show that the asymptotics has qualitatively different form in the quarter-planes of the half-plane $-\\infty<x<\\infty$, $t>0$: (i) for $x<0$, the solution approaches a slowly decaying, modulated wav"},"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":"1906.08489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-20T08:05:10Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"33e0211faa88deda646be91dc2c0abbc1a17ca51eee822e4b5c5ed5195b81b83","abstract_canon_sha256":"ed0fb3d897ee9112343e0b73069eef056809ff9b9dd336d977a9e236aa1ac64f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:35:43.472997Z","signature_b64":"T0+MwqDpAa+WaJPbhWHhLuSEfwosx7K7B8gzJ4eEX7PMfEUWvm67VbmGSXRuAQPAA3S5GQ/HMJGi6uz7j3+IBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d037c119b76d88b842e933dde390289e973ef474424d72a3755b285d0241286","last_reissued_at":"2026-07-05T01:35:43.472374Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:35:43.472374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long-time asymptotics for the integrable nonlocal nonlinear Schr\\\"odinger equation with 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":"2019-06-20T08:05:10Z","abstract_excerpt":"We study the Cauchy problem for the integrable nonlocal nonlinear Schr\\\"odinger (NNLS) equation \\[ iq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\\bar{q}(-x,t)=0 \\] with a step-like initial data: $q(x,0)=q_0(x)$, where $q_0(x)=o(1)$ as $x\\to-\\infty$ and $q_0(x)=A+o(1)$ as $x\\to\\infty$, with an arbitrary positive constant $A>0$. The main aim is to study the long-time behavior of the solution of this problem. 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