{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R4CFA7PZAIR427LITZCMLI337A","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9edf8f1fa7e19af3a28b52515a909e896bac05ca74f72cedec69e573ff6b4e23","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-02-17T16:13:23Z","title_canon_sha256":"1d913cb831fb929f9cb0248acdcc487caa4d7970fb8c8085168080a54608d1b0"},"schema_version":"1.0","source":{"id":"1602.05465","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05465","created_at":"2026-05-18T01:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05465v1","created_at":"2026-05-18T01:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05465","created_at":"2026-05-18T01:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"R4CFA7PZAIR4","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R4CFA7PZAIR427LI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R4CFA7PZ","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:f3b0295e1b2dc6b07fe3c0280efa8f62c662371687ef2d192d1cfbbb5caa95d5","target":"graph","created_at":"2026-05-18T01:06:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Using Hirota's direct method and Baecklund transformations we construct explicit complex one and two-solutions to the complex Korteweg-de Vries equation, the complex modified Korteweg-de Vries equation and the complex sine-Gordon equation. The one-soliton solutions of trigonometric and elliptic type turn out to be PT-symmetric when a constant of integration is chosen to be purely imaginary with one special choice corresponding to solutions recently found by Khare and Saxena. We show that alternatively complex PT-symmetric solutions to the Korteweg-de Vries equation may also be constructed alte","authors_text":"Andreas Fring, Julia Cen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-02-17T16:13:23Z","title":"Complex solitons with real energies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05465","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0c89fed08d182d69a9491c1da7f826e3d39cad27b8e613f6440eed27340f06f1","target":"record","created_at":"2026-05-18T01:06:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9edf8f1fa7e19af3a28b52515a909e896bac05ca74f72cedec69e573ff6b4e23","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-02-17T16:13:23Z","title_canon_sha256":"1d913cb831fb929f9cb0248acdcc487caa4d7970fb8c8085168080a54608d1b0"},"schema_version":"1.0","source":{"id":"1602.05465","kind":"arxiv","version":1}},"canonical_sha256":"8f04507df90223cd7d689e44c5a37bf82d7c7d086772c860c996258995f20798","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f04507df90223cd7d689e44c5a37bf82d7c7d086772c860c996258995f20798","first_computed_at":"2026-05-18T01:06:20.899956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:20.899956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9qz9RjJWW5luGSsPG1Tzx4QXG6p68DZ8Xzb7ufDsjE3HqNFbGS3XCkmiudTDSPO0BPCt8SjTRwXt1I4SByGIDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:20.900481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05465","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c89fed08d182d69a9491c1da7f826e3d39cad27b8e613f6440eed27340f06f1","sha256:f3b0295e1b2dc6b07fe3c0280efa8f62c662371687ef2d192d1cfbbb5caa95d5"],"state_sha256":"444923baa58805f56593dcfa851c3b94dd1482fea4d39f090c8216c6b4fa7bfd"}