{"id":"https://openalex.org/W2075303891","doi":"https://doi.org/10.1137/s0036141000369083","title":"Asymptotically-Free Solutions for the Short-Range Nonlinear Schr\u00f6dinger Equation","display_name":"Asymptotically-Free Solutions for the Short-Range Nonlinear Schr\u00f6dinger Equation","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2075303891","doi":"https://doi.org/10.1137/s0036141000369083","mag":"2075303891"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141000369083","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141000369083","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103015819","display_name":"Kenji Nakanishi","orcid":"https://orcid.org/0000-0002-8988-1726"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kenji Nakanishi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5103015819"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2041,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.91571581,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"32","issue":"6","first_page":"1265","last_page":"1271"},"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":0.9923999905586243,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9729999899864197,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.831966757774353},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6627384424209595},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.6617858409881592},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6137421727180481},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.5565589070320129},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5517263412475586},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.5264164805412292},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.518592357635498},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4972541630268097},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.44711723923683167},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.40004944801330566},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1782672107219696},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15899473428726196}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.831966757774353},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6627384424209595},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.6617858409881592},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6137421727180481},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.5565589070320129},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5517263412475586},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.5264164805412292},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.518592357635498},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4972541630268097},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.44711723923683167},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.40004944801330566},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1782672107219696},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15899473428726196},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036141000369083","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141000369083","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W190761553","https://openalex.org/W1542602023","https://openalex.org/W1584239381","https://openalex.org/W1979262998","https://openalex.org/W1994956606","https://openalex.org/W2022521078","https://openalex.org/W2027879234","https://openalex.org/W2028453580","https://openalex.org/W2047955172","https://openalex.org/W2048877476","https://openalex.org/W2081325709","https://openalex.org/W2084165357","https://openalex.org/W2085669625","https://openalex.org/W2264682811","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2245214771","https://openalex.org/W2073973926","https://openalex.org/W2333053900","https://openalex.org/W1975562467","https://openalex.org/W2951961089","https://openalex.org/W3101208931","https://openalex.org/W2181923191","https://openalex.org/W3213209941","https://openalex.org/W2074095400","https://openalex.org/W1985069144"],"abstract_inverted_index":{"We":[0,19,50],"consider":[1],"the":[2,38,42,54,62],"nonlinear":[3],"Schr\u00f6dinger":[4],"equation":[5],"(NLS)":[6],"with":[7],"a":[8,32],"power":[9,64],"nonlinearity":[10],"|u|p-1u":[11],",":[12],"where":[13],"1":[14],"+":[15,68],"2/n":[16],"<":[17],"p.":[18],"show":[20,52],"that":[21,53],"for":[22,61],"any":[23],"free":[24,39],"solution":[25,33,40],"in":[26,41,58],"L2":[27],"or":[28],"H1":[29],"there":[30],"exists":[31],"of":[34],"NLS":[35],"which":[36],"approaches":[37],"same":[43],"space":[44],"as":[45],"t":[46],"tends":[47],"to":[48],"infinity.":[49],"also":[51],"wave":[55],"operators":[56],"exist":[57],"$\\Sigma^s=H^s\\cap{\\cal":[59],"F}H^s$":[60],"critical":[63],"p":[65],"=":[66],"1+4/(n":[67],"2s).":[69]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-08T07:41:36.138363","created_date":"2025-10-10T00:00:00"}