{"id":"W2006799254","doi":"10.1063/1.2748618","title":"Exact solutions of the Gross-Pitaevskii equation in periodic potential in the presence of external source","year":2007,"lang":"en","type":"article","venue":"Journal of Mathematical Physics","topic":"Cold Atom Physics and Bose-Einstein Condensates","field":"Physics and Astronomy","cited_by":17,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"","keywords":"Elliptic function; Trigonometric functions; Jacobi elliptic functions; Jacobian matrix and determinant; Mathematical analysis; Gross–Pitaevskii equation; Elliptic integral; Mathematics; Quarter period; Elliptic curve; Elliptic rational functions; Trigonometry; Periodic wave; Limit (mathematics); Mathematical physics; Physics; Applied mathematics; Traveling wave; Nonlinear system; Quantum mechanics; Geometry","routes":{"ca_aff":true,"ca_fund":false,"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":[],"consensus_categories":[],"category_scores_codex":[0.0009713441,0.0001071577,0.0002866286,0.00004436608,0.00005638472,0.00002881032,0.0003979173,0.00002767723,0.00003696011],"category_scores_gemma":[0.0000412828,0.00006299999,0.0002456948,0.0002826583,0.0001307399,0.0001662184,0.0000764294,0.0003146275,0.00000200145],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002747257,"about_ca_system_score_gemma":0.00007647438,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004562149,"about_ca_topic_score_gemma":0.000004616866,"domain_scores_codex":[0.9984354,0.0000847246,0.0007064507,0.0000761286,0.0004996647,0.0001976417],"domain_scores_gemma":[0.9986078,0.0004411289,0.0005874632,0.0002122931,0.0001201745,0.00003120607],"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":[0.000179487,0.005317993,0.05049002,0.0003285695,0.0001544463,0.00001464414,0.01518694,0.01094385,0.1558242,0.7151071,0.0001656467,0.04628715],"study_design_scores_gemma":[0.001487526,0.0001787518,0.0563789,0.0008443397,0.0001088843,0.00001143905,0.00327598,0.01841231,0.0266836,0.8923612,0.00003607008,0.0002210295],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8661371,0.00003807067,0.132963,0.000142069,0.00006248978,0.0001351342,0.000003635853,0.000001065437,0.0005173671],"genre_scores_gemma":[0.9993214,0.000001365273,0.0003787664,0.00001282652,0.0002525236,0.000001818767,3.918911e-7,0.00000750713,0.00002340752],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1772541,"threshold_uncertainty_score":0.2569065,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02247954626232708,"score_gpt":0.2648408584859678,"score_spread":0.2423613122236408,"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."}}