{"id":"https://openalex.org/W1992315702","doi":"https://doi.org/10.1016/s0096-3003(03)00569-1","title":"Analytical and numerical studies of the variable-coefficient Gardner equation","display_name":"Analytical and numerical studies of the variable-coefficient Gardner equation","publication_year":2003,"publication_date":"2003-12-04","ids":{"openalex":"https://openalex.org/W1992315702","doi":"https://doi.org/10.1016/s0096-3003(03)00569-1","mag":"1992315702"},"language":"en","primary_location":{"id":"doi:10.1016/s0096-3003(03)00569-1","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(03)00569-1","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","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/A5008935697","display_name":"Ousseynou Nakoulima","orcid":null},"institutions":[{"id":"https://openalex.org/I52585520","display_name":"Universit\u00e9 des Antilles","ror":"https://ror.org/02ryfmr77","country_code":"GP","type":"education","lineage":["https://openalex.org/I52585520"]}],"countries":["GP"],"is_corresponding":false,"raw_author_name":"O. Nakoulima","raw_affiliation_strings":["Faculte des Sciences, Universite des Antilles et de la Guyane, Guadeloupe, Pointe-a-Pitre, France","Faculte des Sciences, Universite des Antilles et de la Guyane, Guadeloupe, Pointe-a-Pitre, France#TAB#"],"affiliations":[{"raw_affiliation_string":"Faculte des Sciences, Universite des Antilles et de la Guyane, Guadeloupe, Pointe-a-Pitre, France","institution_ids":["https://openalex.org/I52585520"]},{"raw_affiliation_string":"Faculte des Sciences, Universite des Antilles et de la Guyane, Guadeloupe, Pointe-a-Pitre, France#TAB#","institution_ids":["https://openalex.org/I52585520"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000089272","display_name":"Narcisse Zahibo","orcid":null},"institutions":[{"id":"https://openalex.org/I52585520","display_name":"Universit\u00e9 des Antilles","ror":"https://ror.org/02ryfmr77","country_code":"GP","type":"education","lineage":["https://openalex.org/I52585520"]}],"countries":["GP"],"is_corresponding":false,"raw_author_name":"N. Zahibo","raw_affiliation_strings":["Faculte des Sciences, Universite des Antilles et de la Guyane, Guadeloupe, Pointe-a-Pitre, France","Faculte des Sciences, Universite des Antilles et de la Guyane, Guadeloupe, Pointe-a-Pitre, France#TAB#"],"affiliations":[{"raw_affiliation_string":"Faculte des Sciences, Universite des Antilles et de la Guyane, Guadeloupe, Pointe-a-Pitre, France","institution_ids":["https://openalex.org/I52585520"]},{"raw_affiliation_string":"Faculte des Sciences, Universite des Antilles et de la Guyane, Guadeloupe, Pointe-a-Pitre, France#TAB#","institution_ids":["https://openalex.org/I52585520"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022054309","display_name":"Efim Pelinovsky","orcid":"https://orcid.org/0000-0002-5092-0302"},"institutions":[{"id":"https://openalex.org/I4210138365","display_name":"Nizhny Novgorod State Technical University","ror":"https://ror.org/037d0vf92","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210138365"]},{"id":"https://openalex.org/I4210161229","display_name":"Institute of Applied Physics","ror":"https://ror.org/05nnv1197","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210096333","https://openalex.org/I4210161229"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"E. Pelinovsky","raw_affiliation_strings":["Applied Mathematics Department, State Technical University, Nizhny Novgorod, Russia","Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia","Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia and Applied Mathematics Department, State Technical University, Nizhny Novgorod, Russia#TAB#"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics Department, State Technical University, Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I4210138365"]},{"raw_affiliation_string":"Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I4210161229"]},{"raw_affiliation_string":"Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia and Applied Mathematics Department, State Technical University, Nizhny Novgorod, Russia#TAB#","institution_ids":["https://openalex.org/I4210161229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035268556","display_name":"Tatiana Talipova","orcid":"https://orcid.org/0000-0002-1967-4174"},"institutions":[{"id":"https://openalex.org/I4210161229","display_name":"Institute of Applied Physics","ror":"https://ror.org/05nnv1197","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210096333","https://openalex.org/I4210161229"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"T. Talipova","raw_affiliation_strings":["Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia","Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I4210161229"]},{"raw_affiliation_string":"Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia#TAB#","institution_ids":["https://openalex.org/I4210161229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062451003","display_name":"Alexey Slunyaev","orcid":"https://orcid.org/0000-0001-7782-2991"},"institutions":[{"id":"https://openalex.org/I4210161229","display_name":"Institute of Applied Physics","ror":"https://ror.org/05nnv1197","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210096333","https://openalex.org/I4210161229"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. Slunyaev","raw_affiliation_strings":["Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia","Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I4210161229"]},{"raw_affiliation_string":"Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia#TAB#","institution_ids":["https://openalex.org/I4210161229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076020566","display_name":"Andrey Kurkin","orcid":"https://orcid.org/0000-0003-3828-6406"},"institutions":[{"id":"https://openalex.org/I47410878","display_name":"Nizhny Novgorod State Pedagogical University","ror":"https://ror.org/05mm0yv21","country_code":"RU","type":"education","lineage":["https://openalex.org/I47410878"]},{"id":"https://openalex.org/I4210138365","display_name":"Nizhny Novgorod State Technical University","ror":"https://ror.org/037d0vf92","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210138365"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. Kurkin","raw_affiliation_strings":["Applied Mathematics Department, State Technical University, Nizhny Novgorod, Russia","Applied Mathematics Department, State Technical University, Nizhny Novgorod, Russia#TAB#"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics Department, State Technical University, Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I4210138365"]},{"raw_affiliation_string":"Applied Mathematics Department, State Technical University, Nizhny Novgorod, Russia#TAB#","institution_ids":["https://openalex.org/I47410878"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5022054309"],"corresponding_institution_ids":["https://openalex.org/I4210138365","https://openalex.org/I4210161229"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.5081,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.64829593,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"152","issue":"2","first_page":"449","last_page":"471"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998000264167786,"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":0.9998000264167786,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9962000250816345,"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/T11061","display_name":"Ocean Waves and Remote Sensing","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5967269539833069},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.5467391014099121},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5316833853721619},{"id":"https://openalex.org/keywords/breather","display_name":"Breather","score":0.5001018047332764},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4306009113788605},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4304755926132202},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.417999804019928},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3615100383758545},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.31591424345970154},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.21362298727035522}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5967269539833069},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.5467391014099121},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5316833853721619},{"id":"https://openalex.org/C74455749","wikidata":"https://www.wikidata.org/wiki/Q5254599","display_name":"Breather","level":3,"score":0.5001018047332764},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4306009113788605},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4304755926132202},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.417999804019928},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3615100383758545},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.31591424345970154},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21362298727035522}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0096-3003(03)00569-1","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(03)00569-1","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W64388182","https://openalex.org/W570834868","https://openalex.org/W1485406846","https://openalex.org/W1510817630","https://openalex.org/W1552987673","https://openalex.org/W1631957514","https://openalex.org/W1668377446","https://openalex.org/W1972643483","https://openalex.org/W1995220437","https://openalex.org/W2000532603","https://openalex.org/W2001958656","https://openalex.org/W2011932509","https://openalex.org/W2013751272","https://openalex.org/W2016034508","https://openalex.org/W2016403827","https://openalex.org/W2020197422","https://openalex.org/W2026006062","https://openalex.org/W2027595215","https://openalex.org/W2030621319","https://openalex.org/W2032031674","https://openalex.org/W2032583666","https://openalex.org/W2037108000","https://openalex.org/W2039981259","https://openalex.org/W2052039877","https://openalex.org/W2052398725","https://openalex.org/W2056105351","https://openalex.org/W2057188184","https://openalex.org/W2081890428","https://openalex.org/W2083960709","https://openalex.org/W2089534605","https://openalex.org/W2094480715","https://openalex.org/W2115600080","https://openalex.org/W2138729229","https://openalex.org/W2912195110","https://openalex.org/W4211036616","https://openalex.org/W4256276137","https://openalex.org/W6602548707","https://openalex.org/W6616347494","https://openalex.org/W6680548384"],"related_works":["https://openalex.org/W2269714044","https://openalex.org/W2026236086","https://openalex.org/W2030584041","https://openalex.org/W3023205431","https://openalex.org/W2036284152","https://openalex.org/W4376111694","https://openalex.org/W1965315336","https://openalex.org/W1953967074","https://openalex.org/W1995435872","https://openalex.org/W2091797280"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
