{"id":"https://openalex.org/W4403535677","doi":"https://doi.org/10.1134/s1995080224603953","title":"On the Integration of the Hierarchy of the Kaup\u2013Boussinesq System with a Self-Consistent Source","display_name":"On the Integration of the Hierarchy of the Kaup\u2013Boussinesq System with a Self-Consistent Source","publication_year":2024,"publication_date":"2024-07-01","ids":{"openalex":"https://openalex.org/W4403535677","doi":"https://doi.org/10.1134/s1995080224603953"},"language":"en","primary_location":{"id":"doi:10.1134/s1995080224603953","doi":"https://doi.org/10.1134/s1995080224603953","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s1995080224603953","pdf_url":null,"source":{"id":"https://openalex.org/S106263159","display_name":"Lobachevskii Journal of Mathematics","issn_l":"1818-9962","issn":["1818-9962","1995-0802"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-d","jufo-1","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lobachevskii Journal of Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5012068496","display_name":"Bazar Atajanovich Babajanov","orcid":"https://orcid.org/0000-0001-6878-791X","observed_orcids":["https://orcid.org/0000-0001-6878-791X"]},"institutions":[{"id":"https://openalex.org/I1302269238","display_name":"Academy of Sciences Republic of Uzbekistan","ror":"https://ror.org/01xgfaw76","country_code":"UZ","type":"government","lineage":["https://openalex.org/I1302269238","https://openalex.org/I4405266844"]},{"id":"https://openalex.org/I14916453","display_name":"Urgench State University","ror":"https://ror.org/0593kfr97","country_code":"UZ","type":"education","lineage":["https://openalex.org/I14916453"]}],"countries":["UZ"],"is_corresponding":true,"raw_author_name":"B. A. Babajanov","raw_affiliation_strings":["Khorezm Branch of Uzbekistan Academy of Sciences, Romanovskii Institute of Mathematics, 220100, Urgench, Uzbekistan","Urgench State University, 220100, Urgench, Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Khorezm Branch of Uzbekistan Academy of Sciences, Romanovskii Institute of Mathematics, 220100, Urgench, Uzbekistan","institution_ids":["https://openalex.org/I1302269238"]},{"raw_affiliation_string":"Urgench State University, 220100, Urgench, Uzbekistan","institution_ids":["https://openalex.org/I14916453"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076278060","display_name":"Fakhriddin Abdikarimov","orcid":"https://orcid.org/0000-0002-2744-8169","observed_orcids":["https://orcid.org/0000-0002-2744-8169"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"F. B. Abdikarimov","raw_affiliation_strings":["Khorezm Mamun Academy, 220900, Khiva, Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Khorezm Mamun Academy, 220900, Khiva, Uzbekistan","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114320070","display_name":"F. U. Sulaymonov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210154340","display_name":"Jizzakh State Pedagogical University","ror":"https://ror.org/05ap1tw43","country_code":"UZ","type":"education","lineage":["https://openalex.org/I4210154340"]}],"countries":["UZ"],"is_corresponding":true,"raw_author_name":"F. U. Sulaymonov","raw_affiliation_strings":["Jizzakh State Pedagogical University, 130100, Jizzakh, Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jizzakh State Pedagogical University, 130100, Jizzakh, Uzbekistan","institution_ids":["https://openalex.org/I4210154340"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012068496","https://openalex.org/A5076278060","https://openalex.org/A5114320070"],"corresponding_institution_ids":["https://openalex.org/I1302269238","https://openalex.org/I14916453","https://openalex.org/I4210154340"],"apc_list":null,"apc_paid":null,"fwci":0.1153,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.22394826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"45","issue":"7","first_page":"3233","last_page":"3245"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994999766349792,"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":0.9994999766349792,"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":0.00039999998989515007,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/self-consistent-sources","display_name":"self-consistent sources","score":0.8849999904632568},{"id":"https://openalex.org/keywords/integrable-hierarchies","display_name":"integrable hierarchies","score":0.7450000047683716},{"id":"https://openalex.org/keywords/sturm-liouville-equation","display_name":"Sturm-Liouville equation","score":0.8849999904632568},{"id":"https://openalex.org/keywords/energy-dependent-potential","display_name":"energy-dependent potential","score":0.9850000143051147},{"id":"https://openalex.org/keywords/direct-scattering-problem","display_name":"direct scattering problem","score":0.7739999890327454},{"id":"https://openalex.org/keywords/inverse-scattering","display_name":"inverse scattering","score":0.9729999899864197},{"id":"https://openalex.org/keywords/nonlinear-evolution-equations","display_name":"nonlinear evolution equations","score":0.5249999761581421}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8888542652130127},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6726576685905457},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38360273838043213},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37062862515449524},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3490660786628723},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3243992328643799},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s1995080224603953","doi":"https://doi.org/10.1134/s1995080224603953","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s1995080224603953","pdf_url":null,"source":{"id":"https://openalex.org/S106263159","display_name":"Lobachevskii Journal of Mathematics","issn_l":"1818-9962","issn":["1818-9962","1995-0802"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-d","jufo-1","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lobachevskii Journal of Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W1964013","https://openalex.org/W100343168","https://openalex.org/W205893080","https://openalex.org/W1501570607","https://openalex.org/W1709021359","https://openalex.org/W1820700137","https://openalex.org/W1964121096","https://openalex.org/W1965033817","https://openalex.org/W1968175892","https://openalex.org/W1974993704","https://openalex.org/W1988379891","https://openalex.org/W1992182052","https://openalex.org/W2006792385","https://openalex.org/W2016479530","https://openalex.org/W2018572930","https://openalex.org/W2025855713","https://openalex.org/W2030669316","https://openalex.org/W2036778679","https://openalex.org/W2040041113","https://openalex.org/W2040663572","https://openalex.org/W2043501979","https://openalex.org/W2044045542","https://openalex.org/W2062381175","https://openalex.org/W2069951189","https://openalex.org/W2079838101","https://openalex.org/W2095300050","https://openalex.org/W2095423784","https://openalex.org/W2140116365","https://openalex.org/W2141172861","https://openalex.org/W2167576285","https://openalex.org/W2259006642","https://openalex.org/W2607355502","https://openalex.org/W2608210418","https://openalex.org/W2612560836","https://openalex.org/W2614263479","https://openalex.org/W2776391851","https://openalex.org/W2964342010","https://openalex.org/W2972038190","https://openalex.org/W2981603323","https://openalex.org/W3017932008","https://openalex.org/W3098606353","https://openalex.org/W3099179356","https://openalex.org/W3104006408","https://openalex.org/W3177447217","https://openalex.org/W3181295917","https://openalex.org/W3189063358","https://openalex.org/W3199155665","https://openalex.org/W4221063294","https://openalex.org/W4282973392","https://openalex.org/W4291291708","https://openalex.org/W4379471526","https://openalex.org/W4385150563","https://openalex.org/W4388000613","https://openalex.org/W4388000654","https://openalex.org/W4390726726","https://openalex.org/W4391297375","https://openalex.org/W7015500448"],"related_works":["https://openalex.org/W4413028856","https://openalex.org/W7222198856","https://openalex.org/W4385150563","https://openalex.org/W2012877515","https://openalex.org/W7207374650","https://openalex.org/W2200682907","https://openalex.org/W2322231512","https://openalex.org/W1964121096","https://openalex.org/W2038467891","https://openalex.org/W800646197"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"article,":[3],"we":[4,49,112],"consider":[5],"a":[6,13,19,26,38,43,92,128],"hierarchy":[7,20,86,122],"of":[8,21,57,68,84,87,100,116,120,123],"the":[9,22,45,51,58,69,73,82,85,88,98,101,108,118,121,124],"Kaup\u2013Boussinesq":[10,23,89,125],"system":[11,24,90,126],"with":[12,25,61,76,81,91,105,127],"self-consistent":[14,27,93,129],"source.":[15,130],"We":[16],"show":[17],"that":[18],"source":[28,94],"is":[29,37,95],"also":[30],"an":[31,62,77,114],"important":[32],"theoretical":[33],"model,":[34],"since":[35],"it":[36],"completely":[39],"integrable":[40],"system.":[41],"For":[42],"solving":[44],"problem":[46,56,104],"under":[47],"consideration,":[48],"use":[50],"direct":[52],"and":[53],"inverse":[54,102],"scattering":[55,70,103,110],"Sturm\u2013Liouville":[59,74],"equation":[60,75],"energy-dependent":[63,78],"potential.":[64],"The":[65],"time":[66],"evolution":[67],"data":[71,111],"for":[72],"potential":[79],"associated":[80],"solution":[83,99,119],"determined.":[96],"Using":[97],"respect":[106],"to":[107],"time-dependent":[109],"give":[113],"algorithm":[115],"constructing":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2024-10-19T00:00:00"}