{"id":"https://openalex.org/W7200219643","doi":null,"title":"\u0422\u043e\u0447\u043d\u0456 \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u043a\u0438 \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u043e\u0433\u043e \u0445\u0432\u0438\u043b\u044c\u043e\u0432\u043e\u0433\u043e \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f","display_name":"\u0422\u043e\u0447\u043d\u0456 \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u043a\u0438 \u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u043e\u0433\u043e \u0445\u0432\u0438\u043b\u044c\u043e\u0432\u043e\u0433\u043e \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W7200219643"},"language":"uk","primary_location":{"id":"pmh:oai:dspace.nuft.edu.ua:123456789/27651","doi":null,"is_oa":true,"landing_page_url":"https://dspace.nuft.edu.ua/handle/123456789/27651","pdf_url":"https://dspace.nuft.edu.ua/bitstreams/f925d1a0-944d-42a6-aef9-0293d279d613/download","source":{"id":"https://openalex.org/S4406922838","display_name":"Institutional Repository of National University of Food Technologies","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Other"},"volume":null,"type":"other","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.nuft.edu.ua/bitstreams/f925d1a0-944d-42a6-aef9-0293d279d613/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5145866750","display_name":"\u0410\u043d\u0430\u0442\u043e\u043b\u0456\u0439 \u0424\u0435\u043e\u0434\u043e\u0441\u0456\u0439\u043e\u0432\u0438\u0447 \u0411\u0430\u0440\u0430\u043d\u043d\u0438\u043a","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"\u0411\u0430\u0440\u0430\u043d\u043d\u0438\u043a, \u0410\u043d\u0430\u0442\u043e\u043b\u0456\u0439 \u0424\u0435\u043e\u0434\u043e\u0441\u0456\u0439\u043e\u0432\u0438\u0447","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024207633","display_name":"T. A. Barannyk","orcid":"https://orcid.org/0009-0003-0509-9935","observed_orcids":["https://orcid.org/0009-0003-0509-9935"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"\u0411\u0430\u0440\u0430\u043d\u043d\u0438\u043a, \u0422\u0435\u0442\u044f\u043d\u0430 \u0410\u043d\u0430\u0442\u043e\u043b\u0456\u0457\u0432\u043d\u0430","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044876309","display_name":"\u0406\u0432\u0430\u043d \u0406\u0432\u0430\u043d\u043e\u0432\u0438\u0447 \u042e\u0440\u0438\u043a","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"\u042e\u0440\u0438\u043a, \u0406\u0432\u0430\u043d \u0406\u0432\u0430\u043d\u043e\u0432\u0438\u0447","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":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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":0.9916999936103821,"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":0.9916999936103821,"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":0.003800000064074993,"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":0.00279999990016222,"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/nonlinear-wave-equations","display_name":"nonlinear wave equations","score":0.9940000176429749},{"id":"https://openalex.org/keywords/exact-solutions","display_name":"exact solutions","score":0.9390000104904175},{"id":"https://openalex.org/keywords/separation-of-variables","display_name":"separation of variables","score":0.9829999804496765}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5253000259399414},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.43880000710487366},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40290001034736633},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.38929998874664307},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3310999870300293},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:dspace.nuft.edu.ua:123456789/27651","doi":null,"is_oa":true,"landing_page_url":"https://dspace.nuft.edu.ua/handle/123456789/27651","pdf_url":"https://dspace.nuft.edu.ua/bitstreams/f925d1a0-944d-42a6-aef9-0293d279d613/download","source":{"id":"https://openalex.org/S4406922838","display_name":"Institutional Repository of National University of Food Technologies","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Other"}],"best_oa_location":{"id":"pmh:oai:dspace.nuft.edu.ua:123456789/27651","doi":null,"is_oa":true,"landing_page_url":"https://dspace.nuft.edu.ua/handle/123456789/27651","pdf_url":"https://dspace.nuft.edu.ua/bitstreams/f925d1a0-944d-42a6-aef9-0293d279d613/download","source":{"id":"https://openalex.org/S4406922838","display_name":"Institutional Repository of National University of Food Technologies","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Other"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7200219643.pdf","grobid_xml":"https://content.openalex.org/works/W7200219643.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7197533250","https://openalex.org/W7198477950","https://openalex.org/W7220598784","https://openalex.org/W7197442956","https://openalex.org/W7220510489","https://openalex.org/W2045247385","https://openalex.org/W7035486643","https://openalex.org/W7220633236","https://openalex.org/W7095975146","https://openalex.org/W7035074006"],"abstract_inverted_index":{"\u0417\u0430\u043f\u0440\u043e\u043f\u043e\u043d\u043e\u0432\u0430\u043d\u0430":[0],"\u0443\u0437\u0430\u0433\u0430\u043b\u044c\u043d\u0435\u043d\u0430":[1],"\u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0430":[2],"\u0440\u043e\u0437\u0434\u0456\u043b\u0435\u043d\u043d\u044f":[3],"\u0437\u043c\u0456\u043d\u043d\u0438\u0445":[4],"\u0434\u043b\u044f":[5],"\u043d\u0435\u043b\u0456\u043d\u0456\u0439\u043d\u0438\u0445":[6],"\u0445\u0432\u0438\u043b\u044c\u043e\u0432\u0438\u0445":[7],"\u0440\u0456\u0432\u043d\u044f\u043d\u044c.":[8,15],"\u041f\u043e\u0431\u0443\u0434\u043e\u0432\u0430\u043d\u0456":[9],"\u0448\u0438\u0440\u043e\u043a\u0456":[10],"\u043a\u043b\u0430\u0441\u0438":[11],"\u0442\u043e\u0447\u043d\u0438\u0445":[12],"\u0440\u043e\u0437\u0432\u2019\u044f\u0437\u043a\u0456\u0432":[13],"\u0446\u0438\u0445":[14],"We":[16],"propose":[17],"a":[18],"generalized":[19],"procedure":[20],"of":[21,23,33,36],"separation":[22],"variables":[24],"for":[25],"nonlinear":[26],"wave":[27],"equations":[28],"and":[29],"construct":[30],"broad":[31],"classes":[32],"exact":[34],"solutions":[35],"these":[37],"equations.":[38]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-07T00:00:00"}
