{"id":"https://openalex.org/W2748839376","doi":"https://doi.org/10.1137/17m1144829","title":"Long Range Scattering for Nonlinear Schr\u00f6dinger Equations with Critical Homogeneous Nonlinearity","display_name":"Long Range Scattering for Nonlinear Schr\u00f6dinger Equations with Critical Homogeneous Nonlinearity","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2748839376","doi":"https://doi.org/10.1137/17m1144829","mag":"2748839376"},"language":"en","primary_location":{"id":"doi:10.1137/17m1144829","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1144829","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/A5028811945","display_name":"Satoshi Masaki","orcid":"https://orcid.org/0000-0003-2582-5108"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Satoshi Masaki","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2582-5108","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055269431","display_name":"Hayato Miyazaki","orcid":"https://orcid.org/0000-0002-4119-3406"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hayato Miyazaki","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4119-3406","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1878,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.85706566,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"50","issue":"3","first_page":"3251","last_page":"3270"},"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":0.9861999750137329,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9825000166893005,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8224263191223145},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7698102593421936},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6691251993179321},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.6440130472183228},{"id":"https://openalex.org/keywords/split-step-method","display_name":"Split-step method","score":0.6084772944450378},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6036760807037354},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5466998815536499},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4936757981777191},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.47641098499298096},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47251614928245544},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.47047287225723267},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4237968325614929},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.3658672571182251},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.1670929193496704},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15174156427383423},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.110192209482193}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8224263191223145},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7698102593421936},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6691251993179321},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.6440130472183228},{"id":"https://openalex.org/C134206417","wikidata":"https://www.wikidata.org/wiki/Q2311789","display_name":"Split-step method","level":3,"score":0.6084772944450378},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6036760807037354},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5466998815536499},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4936757981777191},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.47641098499298096},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47251614928245544},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.47047287225723267},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4237968325614929},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.3658672571182251},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.1670929193496704},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15174156427383423},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.110192209482193},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1144829","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1144829","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1543114419","https://openalex.org/W1979283052","https://openalex.org/W1991493177","https://openalex.org/W1994956606","https://openalex.org/W2033285464","https://openalex.org/W2047955172","https://openalex.org/W2063256635","https://openalex.org/W2064834402","https://openalex.org/W2081325709","https://openalex.org/W2115289219","https://openalex.org/W2122594981","https://openalex.org/W2126407918","https://openalex.org/W2145318670","https://openalex.org/W2163036136","https://openalex.org/W2280344170","https://openalex.org/W2326468819","https://openalex.org/W2327414843","https://openalex.org/W2962857095","https://openalex.org/W2963280826"],"related_works":["https://openalex.org/W2245214771","https://openalex.org/W1521863058","https://openalex.org/W4321141511","https://openalex.org/W4315645228","https://openalex.org/W2333053900","https://openalex.org/W2951961089","https://openalex.org/W3101208931","https://openalex.org/W2181923191","https://openalex.org/W3213209941","https://openalex.org/W1975562467"],"abstract_inverted_index":{"In":[0,108],"this":[1],"paper,":[2],"we":[3,80,110],"consider":[4],"the":[5,10,21,39,42,45,51,54,66,92,105,116,119,123],"final":[6],"state":[7],"problem":[8],"for":[9],"nonlinear":[11],"Schr\u00f6dinger":[12],"equation":[13],"with":[14,76],"a":[15,30,62,70,77,84,88],"homogeneous":[16],"nonlinearity":[17,40,67],"which":[18],"is":[19,27,41,59,99,126],"of":[20,53,104,118],"long":[22],"range":[23],"critical":[24,43],"order":[25],"and":[26,34,87],"not":[28],"necessarily":[29],"polynomial":[31],"in":[32,102,130],"one":[33],"two":[35],"space":[36],"dimensions.":[37],"As":[38],"order,":[44],"possible":[46],"asymptotic":[47],"behavior":[48],"depends":[49],"on":[50,65],"shape":[52],"nonlinearity.":[55],"The":[56],"aim":[57],"here":[58],"to":[60,68,112,115],"give":[61],"sufficient":[63,97],"condition":[64,98],"construct":[69],"modified":[71],"wave":[72],"operator.":[73],"To":[74],"deal":[75],"nonpolynomial":[78],"nonlinearity,":[79],"decompose":[81],"it":[82],"into":[83],"resonant":[85],"part":[86,90,125],"nonresonant":[89,124],"via":[91],"Fourier":[93,106,120],"series":[94],"expansion.":[95],"Our":[96],"then":[100],"given":[101],"terms":[103],"coefficients.":[107],"particular,":[109],"need":[111],"pay":[113],"attention":[114],"decay":[117],"coefficients":[121],"since":[122],"an":[127],"infinite":[128],"sum":[129],"general.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
