{"id":"https://openalex.org/W2986458125","doi":"https://doi.org/10.1137/19m1258402","title":"On Stability of Small Solitons of the 1-D NLS with a Trapping Delta Potential","display_name":"On Stability of Small Solitons of the 1-D NLS with a Trapping Delta Potential","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2986458125","doi":"https://doi.org/10.1137/19m1258402","mag":"2986458125"},"language":"en","primary_location":{"id":"doi:10.1137/19m1258402","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1258402","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arts.units.it/bitstream/11368/2953057/5/Gen_1DNew_Version.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053127593","display_name":"Scipio Cuccagna","orcid":"https://orcid.org/0000-0002-3558-0362"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scipio Cuccagna","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3558-0362","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5057388191","display_name":"Masaya Maeda","orcid":"https://orcid.org/0000-0003-2404-7543"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Masaya Maeda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9197,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.9618763,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"51","issue":"6","first_page":"4311","last_page":"4331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/trapping","display_name":"Trapping","score":0.771111786365509},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7179892063140869},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6524633169174194},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5331045389175415},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5257965922355652},{"id":"https://openalex.org/keywords/virial-theorem","display_name":"Virial theorem","score":0.5040366053581238},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.5036672949790955},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.48345693945884705},{"id":"https://openalex.org/keywords/schr\u00f6dingers-cat","display_name":"Schr\u00f6dinger's cat","score":0.4367271363735199},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4274998903274536},{"id":"https://openalex.org/keywords/delta","display_name":"Delta","score":0.4209459125995636},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2788100838661194},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17627465724945068}],"concepts":[{"id":"https://openalex.org/C2777924906","wikidata":"https://www.wikidata.org/wiki/Q34168","display_name":"Trapping","level":2,"score":0.771111786365509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7179892063140869},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6524633169174194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5331045389175415},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5257965922355652},{"id":"https://openalex.org/C189549420","wikidata":"https://www.wikidata.org/wiki/Q620602","display_name":"Virial theorem","level":3,"score":0.5040366053581238},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.5036672949790955},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.48345693945884705},{"id":"https://openalex.org/C194800363","wikidata":"https://www.wikidata.org/wiki/Q8588","display_name":"Schr\u00f6dinger's cat","level":2,"score":0.4367271363735199},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4274998903274536},{"id":"https://openalex.org/C5072461","wikidata":"https://www.wikidata.org/wiki/Q49506","display_name":"Delta","level":2,"score":0.4209459125995636},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2788100838661194},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17627465724945068},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C98444146","wikidata":"https://www.wikidata.org/wiki/Q318","display_name":"Galaxy","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m1258402","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1258402","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arts.units.it:11368/2953057","is_oa":true,"landing_page_url":"http://hdl.handle.net/11368/2953057","pdf_url":"https://arts.units.it/bitstream/11368/2953057/5/Gen_1DNew_Version.pdf","source":{"id":"https://openalex.org/S4306400480","display_name":"ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142444530","host_organization_name":"University of Trieste","host_organization_lineage":["https://openalex.org/I142444530"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arts.units.it:11368/2953057","is_oa":true,"landing_page_url":"http://hdl.handle.net/11368/2953057","pdf_url":"https://arts.units.it/bitstream/11368/2953057/5/Gen_1DNew_Version.pdf","source":{"id":"https://openalex.org/S4306400480","display_name":"ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142444530","host_organization_name":"University of Trieste","host_organization_lineage":["https://openalex.org/I142444530"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5899999737739563,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G465882141","display_name":null,"funder_award_id":"JP17H02853","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5203992904","display_name":null,"funder_award_id":"FRA 2018","funder_id":"https://openalex.org/F4320327547","funder_display_name":"Universit\u00e0 degli Studi di Trieste"},{"id":"https://openalex.org/G8527378151","display_name":"Study of oscillation phenomena and asymptotic stability of solitons of nonlinear dispersive equations","funder_award_id":"19K03579","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8657881462","display_name":null,"funder_award_id":"JP17H02851","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320327547","display_name":"Universit\u00e0 degli Studi di Trieste","ror":"https://ror.org/02n742c10"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2986458125.pdf","grobid_xml":"https://content.openalex.org/works/W2986458125.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1546223190","https://openalex.org/W1836627485","https://openalex.org/W1921923662","https://openalex.org/W1974691100","https://openalex.org/W1975295150","https://openalex.org/W1978341731","https://openalex.org/W1981394030","https://openalex.org/W1982804467","https://openalex.org/W1990043449","https://openalex.org/W1998939067","https://openalex.org/W2006514031","https://openalex.org/W2026406419","https://openalex.org/W2057288933","https://openalex.org/W2061056514","https://openalex.org/W2065988506","https://openalex.org/W2084357913","https://openalex.org/W2087045446","https://openalex.org/W2087792373","https://openalex.org/W2126203235","https://openalex.org/W2129608986","https://openalex.org/W2142855191","https://openalex.org/W2147378526","https://openalex.org/W2158288051","https://openalex.org/W2164936352","https://openalex.org/W2269390264","https://openalex.org/W2356240368","https://openalex.org/W2490491368","https://openalex.org/W2799474194","https://openalex.org/W2963168266","https://openalex.org/W2963363809","https://openalex.org/W2963750212","https://openalex.org/W2963894642","https://openalex.org/W2964333701","https://openalex.org/W3101591526","https://openalex.org/W3102685768","https://openalex.org/W3103052188","https://openalex.org/W3106290670"],"related_works":["https://openalex.org/W4221046490","https://openalex.org/W4297616267","https://openalex.org/W2502651140","https://openalex.org/W3195406774","https://openalex.org/W4297615481","https://openalex.org/W4297616317","https://openalex.org/W2394289659","https://openalex.org/W4296916267","https://openalex.org/W3111070561","https://openalex.org/W1983117351"],"abstract_inverted_index":{"We":[0,23,52],"consider":[1],"a":[2,8,15,35,55,66],"nonlinear":[3,11],"Schr\u00f6dinger":[4],"equation":[5],"(NLS)":[6],"with":[7,14,65],"very":[9],"general":[10],"term":[12],"and":[13,41],"trapping":[16],"$\\delta":[17],"$":[18],"potential":[19],"on":[20],"the":[21,26,60],"line.":[22],"then":[24],"discuss":[25],"asymptotic":[27],"behavior":[28],"of":[29,49,57,62],"all":[30],"its":[31],"small":[32],"solutions,":[33],"generalizing":[34],"recent":[36],"result":[37,56],"by":[38,47],"Masaki,":[39],"Murphy,":[40],"Segata":[42],"[Anal.":[43],"PDE,":[44],"to":[45],"appear]":[46],"means":[48],"virial-like":[50],"inequalities.":[51],"give":[53],"also":[54],"dispersion":[58],"in":[59],"case":[61],"defocusing":[63],"equations":[64],"nontrapping":[67],"delta":[68],"potential.":[69]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}