{"id":"https://openalex.org/W1965664006","doi":"https://doi.org/10.1137/140955227","title":"Local Existence Theory for Derivative Nonlinear Schr\u00f6dinger Equations with Noninteger Power Nonlinearities","display_name":"Local Existence Theory for Derivative Nonlinear Schr\u00f6dinger Equations with Noninteger Power Nonlinearities","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1965664006","doi":"https://doi.org/10.1137/140955227","mag":"1965664006"},"language":"en","primary_location":{"id":"doi:10.1137/140955227","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140955227","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/1401.7060","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063561103","display_name":"David M. Ambrose","orcid":"https://orcid.org/0000-0003-4753-0319"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"David M. Ambrose","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007235018","display_name":"Gideon Simpson","orcid":"https://orcid.org/0000-0002-2300-6806"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gideon Simpson","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063561103"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.06314692,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"47","issue":"3","first_page":"2241","last_page":"2264"},"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":0.9513000249862671,"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":0.9121999740600586,"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/integer","display_name":"Integer (computer science)","score":0.8384222984313965},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.8129781484603882},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6876502633094788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6047092080116272},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5810987949371338},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.5193294286727905},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4953412115573883},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4944608211517334},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48150572180747986},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4644790589809418},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4566149115562439},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36929023265838623},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3478856086730957},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.30184879899024963},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1582317352294922},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12377998232841492}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.8384222984313965},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.8129781484603882},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6876502633094788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6047092080116272},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5810987949371338},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5193294286727905},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4953412115573883},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4944608211517334},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48150572180747986},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4644790589809418},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4566149115562439},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36929023265838623},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3478856086730957},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30184879899024963},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1582317352294922},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12377998232841492},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/140955227","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140955227","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:1401.7060","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.7060","pdf_url":"https://arxiv.org/pdf/1401.7060","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:1965664006","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1401.7060.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":"pmh:oai:CiteSeerX.psu:10.1.1.756.1597","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.756.1597","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1401.7060.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1401.7060","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1401.7060","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:1401.7060","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.7060","pdf_url":"https://arxiv.org/pdf/1401.7060","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":[{"score":0.8700000047683716,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G5781550132","display_name":"Collaborative Research: Efficient surface-based numerical methods for 3D interfacial flow with surface tension","funder_award_id":"1016267","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7263126401","display_name":"Dispersive PDE and Interfacial Fluid Dynamics","funder_award_id":"1008387","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7721040127","display_name":null,"funder_award_id":"DMS-1016267","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1598079902","https://openalex.org/W1971735108","https://openalex.org/W1981543338","https://openalex.org/W1990258073","https://openalex.org/W2006365463","https://openalex.org/W2008322716","https://openalex.org/W2015581894","https://openalex.org/W2028119371","https://openalex.org/W2032668951","https://openalex.org/W2047689815","https://openalex.org/W2063624047","https://openalex.org/W2068457286","https://openalex.org/W2070013821","https://openalex.org/W2071742362","https://openalex.org/W2078835008","https://openalex.org/W2157662523","https://openalex.org/W2278997551","https://openalex.org/W2596083410","https://openalex.org/W2963870929","https://openalex.org/W3098059678","https://openalex.org/W4213132260"],"related_works":["https://openalex.org/W2953247643","https://openalex.org/W2988907802","https://openalex.org/W2559002103","https://openalex.org/W2949603948","https://openalex.org/W2783500984","https://openalex.org/W2289144935","https://openalex.org/W2952781756","https://openalex.org/W2950345343","https://openalex.org/W2266148834","https://openalex.org/W2271918786","https://openalex.org/W2126022960","https://openalex.org/W2072739261","https://openalex.org/W2582655200","https://openalex.org/W3103216943","https://openalex.org/W2170952935","https://openalex.org/W2962683768","https://openalex.org/W3188494889","https://openalex.org/W3049071471","https://openalex.org/W2950919302","https://openalex.org/W2913920959"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,35,94],"derivative":[3],"nonlinear":[4],"Schr\u00f6dinger":[5],"equation,":[6],"allowing":[7],"noninteger":[8],"powers":[9],"in":[10,26,75],"the":[11,27,39,51,57,60,76,98],"nonlinearity,":[12],"$|u|^{2\\sigma}":[13],"u_x$.":[14],"Our":[15],"main":[16],"theorem":[17],"is":[18,32],"short-time":[19],"existence":[20,52,73],"of":[21,38,53,59],"solutions":[22,54],"with":[23],"initial":[24,45,61,99],"data":[25],"energy":[28,40],"space,":[29],"$H^1;$":[30],"this":[31],"achieved":[33],"by":[34],"careful":[36],"use":[37,88],"method.":[41],"For":[42],"more":[43],"regular":[44],"data,":[46],"we":[47],"establish":[48],"not":[49],"just":[50],"but":[55],"also":[56],"well-posedness":[58],"value":[62],"problem.":[63],"These":[64],"results":[65,74],"hold":[66],"for":[67],"real-valued":[68],"$\\sigma\\geq":[69],"1,$":[70],"while":[71],"prior":[72],"literature":[77],"require":[78],"integer-valued":[79],"$\\sigma$":[80,82],"or":[81,92],"sufficiently":[83],"large":[84],"($\\sigma":[85],"\\geq":[86],"5/2$),":[87],"higher-regularity":[89],"function":[90],"spaces,":[91],"impose":[93],"smallness":[95],"condition":[96],"on":[97],"data.":[100]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}