{"id":"https://openalex.org/W2892178113","doi":"https://doi.org/10.1137/18m1216031","title":"Existence and Stability of Schr\u00f6dinger Solitons on Noncompact Manifolds","display_name":"Existence and Stability of Schr\u00f6dinger Solitons on Noncompact Manifolds","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2892178113","doi":"https://doi.org/10.1137/18m1216031","mag":"2892178113"},"language":"en","primary_location":{"id":"doi:10.1137/18m1216031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1216031","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1809.07643","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023068637","display_name":"David Borthwick","orcid":"https://orcid.org/0000-0002-8221-7355"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Borthwick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044163410","display_name":"Roland Donninger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roland Donninger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022399477","display_name":"Enno Lenzmann","orcid":"https://orcid.org/0000-0002-7627-525X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Enno Lenzmann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055763634","display_name":"Jeremy L. Marzuola","orcid":"https://orcid.org/0000-0002-8668-7143"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jeremy L. Marzuola","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06156632,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"51","issue":"5","first_page":"3854","last_page":"3901"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9952999949455261,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9940999746322632,"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/manifold","display_name":"Manifold (fluid mechanics)","score":0.5989920496940613},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5960965752601624},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5800277590751648},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.549776554107666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5462696552276611},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5301835536956787},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.5223185420036316},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5122207999229431},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5065494775772095},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5051367878913879},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.493460088968277},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48855623602867126},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4279947876930237},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.36910831928253174},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18060895800590515},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11466255784034729}],"concepts":[{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5989920496940613},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5960965752601624},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5800277590751648},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.549776554107666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5462696552276611},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5301835536956787},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.5223185420036316},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5122207999229431},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5065494775772095},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5051367878913879},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.493460088968277},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48855623602867126},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4279947876930237},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36910831928253174},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18060895800590515},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11466255784034729},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/18m1216031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1216031","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:arXiv.org:1809.07643","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.07643","pdf_url":"https://arxiv.org/pdf/1809.07643","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2892178113","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1809.07643.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"mag:3147342486","is_oa":true,"landing_page_url":"https://ui.adsabs.harvard.edu/abs/2018arXiv180907643B/abstract","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:edoc.unibas.ch:75289","is_oa":false,"landing_page_url":"https://edoc.unibas.ch/75289/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401836","display_name":"edoc (University of Basel)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1850255","host_organization_name":"University of Basel","host_organization_lineage":["https://openalex.org/I1850255"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1809.07643","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1809.07643","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1809.07643","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.07643","pdf_url":"https://arxiv.org/pdf/1809.07643","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1300220705","display_name":null,"funder_award_id":"DMS-1352353","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3959103953","display_name":null,"funder_award_id":"P 30076","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4724831252","display_name":null,"funder_award_id":"DMS-1312874","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2892178113.pdf","grobid_xml":"https://content.openalex.org/works/W2892178113.grobid-xml"},"referenced_works_count":69,"referenced_works":["https://openalex.org/W33003989","https://openalex.org/W1481897077","https://openalex.org/W1529742207","https://openalex.org/W1541693388","https://openalex.org/W1575147392","https://openalex.org/W1589231358","https://openalex.org/W1647649584","https://openalex.org/W1680141086","https://openalex.org/W1836627485","https://openalex.org/W1912332091","https://openalex.org/W1966142058","https://openalex.org/W1966652217","https://openalex.org/W1967231068","https://openalex.org/W1970218941","https://openalex.org/W1973235140","https://openalex.org/W1974730313","https://openalex.org/W1977212986","https://openalex.org/W1978341731","https://openalex.org/W1979738097","https://openalex.org/W1982532330","https://openalex.org/W1996483700","https://openalex.org/W2005105370","https://openalex.org/W2006365463","https://openalex.org/W2007591148","https://openalex.org/W2010685312","https://openalex.org/W2015946804","https://openalex.org/W2022978090","https://openalex.org/W2024793963","https://openalex.org/W2044789172","https://openalex.org/W2046022740","https://openalex.org/W2050798497","https://openalex.org/W2051195713","https://openalex.org/W2051980717","https://openalex.org/W2067157000","https://openalex.org/W2069723264","https://openalex.org/W2071132730","https://openalex.org/W2072413694","https://openalex.org/W2074948932","https://openalex.org/W2077993194","https://openalex.org/W2081065853","https://openalex.org/W2084357913","https://openalex.org/W2087792373","https://openalex.org/W2091052151","https://openalex.org/W2092795994","https://openalex.org/W2103691817","https://openalex.org/W2109528362","https://openalex.org/W2127099082","https://openalex.org/W2135269829","https://openalex.org/W2148603137","https://openalex.org/W2149981483","https://openalex.org/W2151949034","https://openalex.org/W2325412313","https://openalex.org/W2432644127","https://openalex.org/W2482762127","https://openalex.org/W2579246540","https://openalex.org/W2582151313","https://openalex.org/W2951712192","https://openalex.org/W2963110420","https://openalex.org/W2963237143","https://openalex.org/W2963348584","https://openalex.org/W2963787058","https://openalex.org/W2963812874","https://openalex.org/W3098585723","https://openalex.org/W3099522555","https://openalex.org/W3104151178","https://openalex.org/W3105821456","https://openalex.org/W3125805082","https://openalex.org/W3217362339","https://openalex.org/W4213132260"],"related_works":["https://openalex.org/W1600048908","https://openalex.org/W3149068669","https://openalex.org/W3095461468","https://openalex.org/W2296511311","https://openalex.org/W937687007","https://openalex.org/W2900821120","https://openalex.org/W2737400320","https://openalex.org/W2787959410","https://openalex.org/W2963879384","https://openalex.org/W2012585369","https://openalex.org/W2952976634","https://openalex.org/W2996922893","https://openalex.org/W2113443148","https://openalex.org/W3199756976","https://openalex.org/W3202480205","https://openalex.org/W3059551493","https://openalex.org/W2921442358","https://openalex.org/W2001751927","https://openalex.org/W2751621638","https://openalex.org/W2337080519"],"abstract_inverted_index":{"We":[0,16,120],"consider":[1],"the":[2,18,27,34,37,48,54,59,73,80,91,94,98,101,114,134],"focusing":[3],"nonlinear":[4],"Schr\u00f6dinger":[5],"equation":[6],"on":[7],"a":[8,21,76,84],"large":[9],"class":[10],"of":[11,20,36,47,65,75,87,90,93,100,117],"rotationally":[12],"symmetric,":[13],"noncompact":[14],"manifolds.":[15],"prove":[17],"existence":[19],"solitary":[22,38,81],"wave":[23,39,82],"by":[24,43,57],"perturbing":[25],"off":[26],"flat":[28],"Euclidean":[29],"case.":[30],"Furthermore,":[31],"we":[32,67],"study":[33],"stability":[35],"under":[40,127],"radial":[41],"perturbations":[42],"analyzing":[44],"spectral":[45,142],"properties":[46,143],"associated":[49],"linearized":[50],"operator.":[51],"Finally,":[52],"in":[53,83,145],"L2-critical":[55],"case,":[56],"considering":[58],"Vakhitov--Kolokolov":[60,135],"criterion":[61],"(see":[62],"also":[63,121],"results":[64,116],"Grillakis--Shatah--Strauss),":[66],"provide":[68,122],"numerical":[69,123],"evidence":[70,124],"showing":[71],"that":[72],"introduction":[74],"nontrivial":[77],"geometry":[78],"destabilizes":[79],"wide":[85],"variety":[86],"cases,":[88],"regardless":[89],"curvature":[92],"manifold.":[95],"In":[96],"particular,":[97],"parameters":[99],"metric":[102],"corresponding":[103],"to":[104,110,137],"standard":[105],"hyperbolic":[106],"space":[107],"will":[108],"lead":[109],"instability":[111],"consistent":[112],"with":[113],"blow-up":[115],"Banica--Duyckaerts":[118],"(2015).":[119],"for":[125,133],"geometries":[126],"which":[128],"it":[129],"would":[130],"be":[131],"possible":[132],"condition":[136],"suggest":[138],"stability,":[139],"provided":[140],"certain":[141],"hold":[144],"these":[146],"spaces.":[147]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}