{"id":"W2050492749","doi":"10.3934/cpaa.2008.7.193","title":"Existence of unstable standing waves for the inhomogeneous nonlinear Schrödinger equation","year":2008,"lang":"en","type":"article","venue":"Communications on Pure &amp Applied Analysis","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Standing wave; Physics; Nonlinear Schrödinger equation; Nonlinear system; Homogeneous; Mathematical physics; Schrödinger equation; Instability; Mathematical analysis; Classical mechanics; Mathematics; Quantum mechanics; Thermodynamics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005696535,0.0005681571,0.0003581721,0.0009193394,0.0009129933,0.00111692,0.0006766368,0.0006277592,0.001996984],"category_scores_gemma":[0.001768109,0.0002506067,0.0005096539,0.0002944859,0.001015996,0.001285304,0.001360484,0.0009783696,0.0003818319],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000521314,"about_ca_system_score_gemma":0.0004325812,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005968661,"about_ca_topic_score_gemma":0.0003709263,"domain_scores_codex":[0.9998317,0.00003667999,0.00001291424,0.00002474733,0.00006219461,0.0000317659],"domain_scores_gemma":[0.9991531,0.0002517645,0.0001861572,0.00004909303,0.0002169216,0.000142984],"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":[0.0002023255,0.00005104908,0.002586177,0.0001482749,0.00005013958,0.0009842253,0.0008183564,0.01961146,0.1017661,0.8591533,0.001836914,0.01279169],"study_design_scores_gemma":[0.00008573475,0.0002191806,0.00223856,0.00004263776,0.00004778834,0.0008697967,0.0003898703,0.6196776,0.03274953,0.3401517,0.003438642,0.00008897208],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6237137,0.0006200425,0.3519013,0.0008943964,0.0001109398,0.00009761448,0.0001358553,0.000171858,0.02235427],"genre_scores_gemma":[0.9678301,0.0003744462,0.02261386,0.0001667282,0.00008489744,0.0001165568,0.0001128185,0.00004271771,0.008657868],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.001996984,"threshold_uncertainty_score":0.006680608,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2176088815530308,"score_gpt":0.3709009605686659,"score_spread":0.1532920790156351,"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."}}