{"id":"https://openalex.org/W1963932366","doi":"https://doi.org/10.1137/12089956x","title":"Modified Scattering Operator for the Derivative Nonlinear Schr\u00f6dinger Equation","display_name":"Modified Scattering Operator for the Derivative Nonlinear Schr\u00f6dinger Equation","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1963932366","doi":"https://doi.org/10.1137/12089956x","mag":"1963932366"},"language":"en","primary_location":{"id":"doi:10.1137/12089956x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/12089956x","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/A5014535747","display_name":"Zihua Guo","orcid":"https://orcid.org/0000-0002-5319-7906"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zihua Guo","raw_affiliation_strings":["Peking University"],"affiliations":[{"raw_affiliation_string":"Peking University","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041326220","display_name":"Nakao Hayashi","orcid":"https://orcid.org/0000-0002-4622-1867"},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"Osaka University","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Nakao Hayashi","raw_affiliation_strings":["Osaka University"],"affiliations":[{"raw_affiliation_string":"Osaka University","institution_ids":["https://openalex.org/I98285908"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003390354","display_name":"Yiquan Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiquan Lin","raw_affiliation_strings":["Peking University"],"affiliations":[{"raw_affiliation_string":"Peking University","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084597974","display_name":"Pavel I. Naumkin","orcid":null},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Pavel I. Naumkin","raw_affiliation_strings":["Universidad Nacional Aut\u00f3noma de M\u00e9xico (National Autonomous University of Mexico)"],"affiliations":[{"raw_affiliation_string":"Universidad Nacional Aut\u00f3noma de M\u00e9xico (National Autonomous University of Mexico)","institution_ids":["https://openalex.org/I8961855"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5014535747"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":null,"apc_paid":null,"fwci":1.3077,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.75322463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"45","issue":"6","first_page":"3854","last_page":"3871"},"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":0.9871000051498413,"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":0.9868000149726868,"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/sobolev-space","display_name":"Sobolev space","score":0.8089110851287842},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6330113410949707},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.5516039133071899},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5402652025222778},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.4769512712955475},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.47102388739585876},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46848854422569275},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45244142413139343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4309764802455902},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.3945838510990143},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32748913764953613},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.20028182864189148},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06556189060211182}],"concepts":[{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.8089110851287842},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6330113410949707},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5516039133071899},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5402652025222778},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.4769512712955475},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.47102388739585876},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46848854422569275},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45244142413139343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4309764802455902},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.3945838510990143},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32748913764953613},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20028182864189148},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06556189060211182},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/12089956x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/12089956x","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":16,"referenced_works":["https://openalex.org/W1592146221","https://openalex.org/W1826826645","https://openalex.org/W1971735108","https://openalex.org/W1985247483","https://openalex.org/W2016037919","https://openalex.org/W2019167396","https://openalex.org/W2021643216","https://openalex.org/W2034648836","https://openalex.org/W2034680690","https://openalex.org/W2066935708","https://openalex.org/W2068457286","https://openalex.org/W2078835008","https://openalex.org/W2081325709","https://openalex.org/W2084421172","https://openalex.org/W2087393841","https://openalex.org/W2169431613"],"related_works":["https://openalex.org/W4299978068","https://openalex.org/W2164189677","https://openalex.org/W2245214771","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"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,18,28,31,36,39],"derivative":[3],"nonlinear":[4],"Schr\u00f6dinger":[5],"equation":[6],"$i\\partial_{t}u+\\frac{1}{2}\\partial_{x}^{2}u=i\\partial_{x}(|u|^{2}u)$,":[7],"$t\\in":[8],"\\mathbf{R}$,":[9],"$x\\in":[10],"\\mathbf{R}$.":[11],"Our":[12],"purpose":[13],"is":[14,22,48,54],"to":[15,35],"prove":[16],"that":[17],"modified":[19],"scattering":[20],"operator":[21],"defined":[23,55],"as":[24],"a":[25],"map":[26],"from":[27],"neighborhood":[29,37],"of":[30,38],"origin":[32,40],"in":[33,41],"$\\mathbf{H}^{1,\\alpha+\\gamma}$":[34],"$\\mathbf{H}^{1,\\alpha},$":[42],"where":[43],"$\\alpha":[44],">\\frac{1}{2}$":[45],"and":[46],"$\\gamma>0$":[47],"small.":[49],"The":[50],"weighted":[51],"Sobolev":[52],"space":[53],"by":[56],"$\\mathbf{H}^{m,s}=\\{\\phi\\in":[57],"\\mathbf{L}^{2};\\|(1+x^{2})^{\\frac{s}{2}}(1-\\partial_{x}^{2})^{\\frac{m}{2}}\\phi":[58],"\\|_{\\mathbf{L}^{2}}<\\infty\\}.$":[59]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}