{"id":"https://openalex.org/W1704271194","doi":"https://doi.org/10.1137/151004926","title":"Soliton Theory and Hankel Operators","display_name":"Soliton Theory and Hankel Operators","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1704271194","doi":"https://doi.org/10.1137/151004926","mag":"1704271194"},"language":"en","primary_location":{"id":"doi:10.1137/151004926","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151004926","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1310.3873","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034826106","display_name":"Sergei M. Grudsky","orcid":"https://orcid.org/0000-0002-3748-5449"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sergei Grudsky","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5024510770","display_name":"Alexei Rybkin","orcid":"https://orcid.org/0000-0001-7731-0937"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexei Rybkin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.03795393,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"47","issue":"3","first_page":"2283","last_page":"2323"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9997000098228455,"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":0.9991000294685364,"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/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.7912170886993408},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.7463034987449646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6506528258323669},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6391287446022034},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.5768185257911682},{"id":"https://openalex.org/keywords/hankel-matrix","display_name":"Hankel matrix","score":0.5393412709236145},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5337783694267273},{"id":"https://openalex.org/keywords/hankel-transform","display_name":"Hankel transform","score":0.4959636628627777},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.4950663149356842},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4347516596317291},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4056466817855835},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3739243149757385},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3629416823387146},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15094012022018433},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12455615401268005},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10560792684555054},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.08085563778877258}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.7912170886993408},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.7463034987449646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6506528258323669},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6391287446022034},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.5768185257911682},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.5393412709236145},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5337783694267273},{"id":"https://openalex.org/C57640460","wikidata":"https://www.wikidata.org/wiki/Q155208","display_name":"Hankel transform","level":3,"score":0.4959636628627777},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.4950663149356842},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4347516596317291},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4056466817855835},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3739243149757385},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3629416823387146},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15094012022018433},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12455615401268005},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10560792684555054},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.08085563778877258},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/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":5,"locations":[{"id":"doi:10.1137/151004926","is_oa":false,"landing_page_url":"https://doi.org/10.1137/151004926","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:1310.3873","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.3873","pdf_url":"https://arxiv.org/pdf/1310.3873","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:1704271194","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1310.3873","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:10.1.1.742.1701","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.742.1701","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/1310.3873.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1310.3873","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1310.3873","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1310.3873","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1310.3873","pdf_url":"https://arxiv.org/pdf/1310.3873","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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/G1422510818","display_name":"Inverse Scattering Transform and non-decaying solutions of completely integrable nonlinear PDE's","funder_award_id":"1009673","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1704271194.pdf","grobid_xml":"https://content.openalex.org/works/W1704271194.grobid-xml"},"referenced_works_count":72,"referenced_works":["https://openalex.org/W47028002","https://openalex.org/W100101518","https://openalex.org/W176163197","https://openalex.org/W206143723","https://openalex.org/W1500190377","https://openalex.org/W1539173981","https://openalex.org/W1547431580","https://openalex.org/W1553471577","https://openalex.org/W1573599061","https://openalex.org/W1591238430","https://openalex.org/W1597741994","https://openalex.org/W1599355377","https://openalex.org/W1624518749","https://openalex.org/W1858761365","https://openalex.org/W1874715226","https://openalex.org/W1968405112","https://openalex.org/W1968804801","https://openalex.org/W1970276872","https://openalex.org/W1973107894","https://openalex.org/W1977887872","https://openalex.org/W1984778623","https://openalex.org/W1989456241","https://openalex.org/W1989760690","https://openalex.org/W1990096242","https://openalex.org/W1990702143","https://openalex.org/W1994531102","https://openalex.org/W1997632432","https://openalex.org/W1998263057","https://openalex.org/W2003485783","https://openalex.org/W2007694075","https://openalex.org/W2009917801","https://openalex.org/W2011745171","https://openalex.org/W2012962733","https://openalex.org/W2014817276","https://openalex.org/W2016568957","https://openalex.org/W2023780826","https://openalex.org/W2036185015","https://openalex.org/W2043034065","https://openalex.org/W2048718239","https://openalex.org/W2049208166","https://openalex.org/W2055201608","https://openalex.org/W2059841798","https://openalex.org/W2062565740","https://openalex.org/W2063185735","https://openalex.org/W2064420703","https://openalex.org/W2064425372","https://openalex.org/W2077191608","https://openalex.org/W2077312461","https://openalex.org/W2080526571","https://openalex.org/W2083960709","https://openalex.org/W2091947763","https://openalex.org/W2092327885","https://openalex.org/W2093667022","https://openalex.org/W2104369108","https://openalex.org/W2109453208","https://openalex.org/W2115032357","https://openalex.org/W2139145457","https://openalex.org/W2141766250","https://openalex.org/W2183692121","https://openalex.org/W2229416648","https://openalex.org/W2330732766","https://openalex.org/W2378380450","https://openalex.org/W2475789720","https://openalex.org/W2731771262","https://openalex.org/W2951868104","https://openalex.org/W2997641768","https://openalex.org/W3035365041","https://openalex.org/W3100591295","https://openalex.org/W3101261702","https://openalex.org/W3105378887","https://openalex.org/W3105909549","https://openalex.org/W4247381331"],"related_works":["https://openalex.org/W2952347826","https://openalex.org/W3181324063","https://openalex.org/W3190341910","https://openalex.org/W3101626933","https://openalex.org/W2991539229","https://openalex.org/W2987997774","https://openalex.org/W3125805082","https://openalex.org/W215500189","https://openalex.org/W2974405085","https://openalex.org/W2963607086","https://openalex.org/W3135785692","https://openalex.org/W150158519","https://openalex.org/W3149307788","https://openalex.org/W2955180423","https://openalex.org/W2095410283","https://openalex.org/W3001243918","https://openalex.org/W2768535366","https://openalex.org/W2021003071","https://openalex.org/W2166252539","https://openalex.org/W2181686443"],"abstract_inverted_index":{"Soliton":[0],"theory":[1,4],"and":[2,27],"the":[3,32,36,40,47,50,64,68,73,77,103],"of":[5,35,49,52,63,94],"Hankel":[6,53,115],"(and":[7],"Toeplitz)":[8],"operators":[9,54],"have":[10],"stayed":[11],"essentially":[12],"hermetic":[13],"to":[14,84,91],"each":[15],"other.":[16],"This":[17,80],"paper":[18],"is":[19],"concerned":[20],"with":[21,72],"linking":[22],"these":[23],"two":[24],"very":[25],"active":[26],"extremely":[28],"large":[29],"theories.":[30],"On":[31],"prototypical":[33],"example":[34],"Cauchy":[37],"problem":[38],"for":[39,67,76,114],"Korteweg--de":[41],"Vries":[42],"(KdV)":[43],"equation":[44],"we":[45],"demonstrate":[46],"power":[48],"language":[51],"in":[55,61],"which":[56,106],"symbols":[57],"are":[58,107],"conveniently":[59],"represented":[60],"terms":[62],"scattering":[65],"data":[66,75],"Schr\u00f6dinger":[69],"operator":[70],"associated":[71],"initial":[74,104],"KdV":[78],"equation.":[79],"approach":[81],"yields":[82],"short-cuts":[83],"already":[85],"known":[86],"results":[87,113],"as":[88,90],"well":[89],"a":[92],"variety":[93],"new":[95],"ones":[96],"(e.g.,":[97],"wellposedness":[98],"beyond":[99],"standard":[100],"assumptions":[101],"on":[102],"data)":[105],"achieved":[108],"by":[109],"employing":[110],"some":[111],"subtle":[112],"operators.":[116]},"counts_by_year":[],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}