{"id":"https://openalex.org/W7225326562","doi":"https://doi.org/10.5281/zenodo.23975766","title":"OF THE LAX REPRESENTATION OF THE DERIVATIVE NONLINEAR SCHR\u00d6DINGER EQUATION USING THE KAUP\u2013NEWELL SPECTRAL PROBLEM","display_name":"OF THE LAX REPRESENTATION OF THE DERIVATIVE NONLINEAR SCHR\u00d6DINGER EQUATION USING THE KAUP\u2013NEWELL SPECTRAL PROBLEM","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225326562","doi":"https://doi.org/10.5281/zenodo.23975766"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23975766","doi":"https://doi.org/10.5281/zenodo.23975766","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23975766","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23975766","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160843659","display_name":"Hamdam Ergash o\u02bbg\u02bbli Yakubov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yakubov, Hamdam Ergash ogli","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160739306","display_name":"Islom Ikramovich Xusainov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xusainov, Islom Ikramovich","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160811885","display_name":"Elyor Alimboyevich Shamuratov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shamuratov, Elyor Alimboyevich","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5160813865","display_name":"Askarbek Gayrat o'g'li Husainov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Husainov, Askarbek Gayrat o'g'li","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":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.8755000233650208,"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"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.8755000233650208,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.12229999899864197,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/derivative-nonlinear-schrodinger-equation","display_name":"derivative nonlinear Schr\u00f6dinger equation","score":0.9950000047683716},{"id":"https://openalex.org/keywords/lax-representation","display_name":"Lax representation","score":0.7369999885559082},{"id":"https://openalex.org/keywords/spectral-theory","display_name":"spectral theory","score":0.48899999260902405},{"id":"https://openalex.org/keywords/rapidly-decreasing-functions","display_name":"rapidly decreasing functions","score":0.5569999814033508},{"id":"https://openalex.org/keywords/schwartz-space","display_name":"Schwartz space","score":0.9539999961853027},{"id":"https://openalex.org/keywords/solution-estimates","display_name":"solution estimates","score":0.5059999823570251},{"id":"https://openalex.org/keywords/smoothness-of-solutions","display_name":"smoothness of solutions","score":0.8230000138282776},{"id":"https://openalex.org/keywords/infinite-domains","display_name":"infinite domains","score":0.40400001406669617}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6428999900817871},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6322000026702881},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5011000037193298},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49810001254081726},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4925999939441681},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4781999886035919},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.47099998593330383},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43689998984336853},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.38040000200271606},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.36660000681877136},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.34279999136924744},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C172829509","wikidata":"https://www.wikidata.org/wiki/Q4115796","display_name":"Lax pair","level":3,"score":0.3230000138282776},{"id":"https://openalex.org/C184537036","wikidata":"https://www.wikidata.org/wiki/Q14163503","display_name":"Generalizations of the derivative","level":3,"score":0.32260000705718994},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.296099990606308},{"id":"https://openalex.org/C134206417","wikidata":"https://www.wikidata.org/wiki/Q2311789","display_name":"Split-step method","level":3,"score":0.28760001063346863},{"id":"https://openalex.org/C200602138","wikidata":"https://www.wikidata.org/wiki/Q16979193","display_name":"Independent equation","level":3,"score":0.2870999872684479},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C78340151","wikidata":"https://www.wikidata.org/wiki/Q2621220","display_name":"Functional derivative","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C2985105764","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral function","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C33257320","wikidata":"https://www.wikidata.org/wiki/Q1932744","display_name":"Second derivative","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23975766","doi":"https://doi.org/10.5281/zenodo.23975766","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23975766","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"},{"id":"doi:10.5281/zenodo.23975767","doi":"https://doi.org/10.5281/zenodo.23975767","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23975767","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23975766","doi":"https://doi.org/10.5281/zenodo.23975766","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23975766","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225292487","https://openalex.org/W1981543338","https://openalex.org/W1027911479","https://openalex.org/W3113756329","https://openalex.org/W4310861946","https://openalex.org/W2313333291","https://openalex.org/W1971735108","https://openalex.org/W2115448586","https://openalex.org/W2324756930","https://openalex.org/W2070879083"],"abstract_inverted_index":{"In":[0],"modern":[1],"mathematical":[2],"physics":[3],"and":[4,35,62,87],"the":[5,11,40,50,70,73,84,90],"theory":[6],"of":[7,13,42,52,59,72,89],"nonlinear":[8,33],"differential":[9],"equations,":[10],"study":[12],"Schr\u00f6dinger-type":[14],"equations":[15,23,44],"plays":[16],"a":[17],"crucial":[18],"role.":[19],"Specifically,":[20],"derivative":[21,74],"Schr\u00f6dinger":[22,75],"are":[24],"widely":[25],"used":[26],"to":[27,69],"model":[28],"quantum":[29],"mechanics,":[30],"plasma":[31],"physics,":[32],"optics,":[34],"various":[36],"wave":[37],"phenomena.":[38],"Investigating":[39],"solutions":[41],"such":[43],"in":[45],"infinite":[46],"domains,":[47],"particularly":[48],"within":[49,77],"class":[51],"rapidly":[53],"decreasing":[54],"functions":[55],"(Schwartz":[56],"space),":[57],"is":[58,67],"significant":[60],"theoretical":[61],"practical":[63],"interest.":[64],"This":[65],"paper":[66],"devoted":[68],"integration":[71],"equation":[76],"this":[78],"specific":[79],"function":[80],"class,":[81],"thoroughly":[82],"analyzing":[83],"smoothness,":[85],"behavior,":[86],"estimates":[88],"solutions.":[91]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}