{"id":"W4387170236","doi":"10.1007/s00023-023-01370-6","title":"Pitchfork Bifurcation at Line Solitons for Nonlinear Schrödinger Equations on the Product Space $${\\mathbb {R}}\\times {\\mathbb {T}}$$","year":2023,"lang":"en","type":"article","venue":"Annales Henri Poincaré","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Bifurcation; Soliton; Nonlinear system; Bifurcation theory; Space (punctuation); Product (mathematics); Line (geometry); Mathematical physics; Nonlinear Schrödinger equation; Pitchfork bifurcation; Mathematical analysis; Real line; Physics; Schrödinger equation; Quantum mechanics; Geometry; Computer science","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001147715,0.0004417745,0.0004947255,0.0001988422,0.0007730845,0.00008868435,0.0005081212,0.0001219979,0.00008899857],"category_scores_gemma":[0.003722724,0.0003220385,0.0003223976,0.0008442854,0.0001943528,0.0002668251,0.0002756567,0.0003277507,0.001550292],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001396878,"about_ca_system_score_gemma":0.0001143722,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004489145,"about_ca_topic_score_gemma":0.00001738698,"domain_scores_codex":[0.9971741,0.0001044317,0.0006890881,0.0006489024,0.0006063389,0.0007771201],"domain_scores_gemma":[0.992959,0.004891129,0.0003776445,0.001241231,0.0003766333,0.0001544164],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00005703118,0.000383768,0.00001082347,0.0004611444,0.0001271478,0.000003074664,0.001585096,0.000610831,0.005279023,0.9157344,0.07469281,0.001054859],"study_design_scores_gemma":[0.0004589213,0.0001872417,0.00002072598,0.0002497983,0.0001093455,0.000005355012,0.0003215858,0.02695812,0.01818904,0.9282274,0.02480203,0.0004703993],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4644579,0.001005929,0.2949262,0.1820156,0.00199384,0.01809343,0.001481703,0.006028456,0.02999688],"genre_scores_gemma":[0.7905787,0.0003036229,0.141516,0.002302898,0.003395667,0.003579805,0.0009762438,0.0007873762,0.05655973],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3261207,"threshold_uncertainty_score":0.9999232,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1069712108993242,"score_gpt":0.3618887873688568,"score_spread":0.2549175764695326,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}