{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:D3EGNXCCKRBG7UO5XLPKTPTR67","short_pith_number":"pith:D3EGNXCC","schema_version":"1.0","canonical_sha256":"1ec866dc4254426fd1ddbadea9be71f7de933d7315bd0c837385b6f5a9a48f9e","source":{"kind":"arxiv","id":"1103.2672","version":1},"attestation_state":"computed","paper":{"title":"Gaussian pulse dynamics in gain media with Kerr nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Christian Jirauschek, Franz X. K\\\"artner","submitted_at":"2011-03-14T14:09:34Z","abstract_excerpt":"Using the Kantorovitch method in combination with a Gaussian ansatz, we derive the equations of motion for spatial, temporal and spatiotemporal optical propagation in a dispersive Kerr medium with a general transverse and spectral gain profile. By rewriting the variational equations as differential equations for the temporal and spatial Gaussian q parameters, optical ABCD matrices for the Kerr effect, a general transverse gain profile and nonparabolic spectral gain filtering are obtained. Further effects can easily be taken into account by adding the corresponding ABCD matrices. Applications i"},"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":"1103.2672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2011-03-14T14:09:34Z","cross_cats_sorted":[],"title_canon_sha256":"6f608b8538192b393d942146f9cc39dcf0b849bcf2d6968f6e8f58f384f247df","abstract_canon_sha256":"49af77091abb353a14a16ad1df86b674bd34f6a7a4a8322617b8a342e4c3a271"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:54.391524Z","signature_b64":"zM+T+eYipy3jUdtX2FMh5NwPrHHUjNx3TXfMHHakdFPq7zbMP+vvG5mZsW6H2DOJ/CvIqEF0rYh6K0qWe86BDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ec866dc4254426fd1ddbadea9be71f7de933d7315bd0c837385b6f5a9a48f9e","last_reissued_at":"2026-05-18T04:26:54.390844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:54.390844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gaussian pulse dynamics in gain media with Kerr nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Christian Jirauschek, Franz X. K\\\"artner","submitted_at":"2011-03-14T14:09:34Z","abstract_excerpt":"Using the Kantorovitch method in combination with a Gaussian ansatz, we derive the equations of motion for spatial, temporal and spatiotemporal optical propagation in a dispersive Kerr medium with a general transverse and spectral gain profile. By rewriting the variational equations as differential equations for the temporal and spatial Gaussian q parameters, optical ABCD matrices for the Kerr effect, a general transverse gain profile and nonparabolic spectral gain filtering are obtained. Further effects can easily be taken into account by adding the corresponding ABCD matrices. Applications i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2672","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1103.2672","created_at":"2026-05-18T04:26:54.390958+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.2672v1","created_at":"2026-05-18T04:26:54.390958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2672","created_at":"2026-05-18T04:26:54.390958+00:00"},{"alias_kind":"pith_short_12","alias_value":"D3EGNXCCKRBG","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"D3EGNXCCKRBG7UO5","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"D3EGNXCC","created_at":"2026-05-18T12:26:26.731475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67","json":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67.json","graph_json":"https://pith.science/api/pith-number/D3EGNXCCKRBG7UO5XLPKTPTR67/graph.json","events_json":"https://pith.science/api/pith-number/D3EGNXCCKRBG7UO5XLPKTPTR67/events.json","paper":"https://pith.science/paper/D3EGNXCC"},"agent_actions":{"view_html":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67","download_json":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67.json","view_paper":"https://pith.science/paper/D3EGNXCC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.2672&json=true","fetch_graph":"https://pith.science/api/pith-number/D3EGNXCCKRBG7UO5XLPKTPTR67/graph.json","fetch_events":"https://pith.science/api/pith-number/D3EGNXCCKRBG7UO5XLPKTPTR67/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/action/storage_attestation","attest_author":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/action/author_attestation","sign_citation":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/action/citation_signature","submit_replication":"https://pith.science/pith/D3EGNXCCKRBG7UO5XLPKTPTR67/action/replication_record"}},"created_at":"2026-05-18T04:26:54.390958+00:00","updated_at":"2026-05-18T04:26:54.390958+00:00"}