{"id":"https://openalex.org/W2989827099","doi":"https://doi.org/10.1155/2019/9314693","title":"Searching for Analytical Solutions of the (2+1)\u2010Dimensional KP Equation by Two Different Systematic Methods","display_name":"Searching for Analytical Solutions of the (2+1)\u2010Dimensional KP Equation by Two Different Systematic Methods","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2989827099","doi":"https://doi.org/10.1155/2019/9314693","mag":"2989827099"},"language":"en","primary_location":{"id":"doi:10.1155/2019/9314693","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/9314693","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/9314693.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2019/9314693.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084985048","display_name":"Yongyi Gu","orcid":"https://orcid.org/0000-0002-6651-1714"},"institutions":[{"id":"https://openalex.org/I201459984","display_name":"Guangdong University Of Finances and Economics","ror":"https://ror.org/0459pv085","country_code":"CN","type":"education","lineage":["https://openalex.org/I201459984"]},{"id":"https://openalex.org/I4210088341","display_name":"University of Finance and Economics","ror":"https://ror.org/005d8s603","country_code":"MN","type":"education","lineage":["https://openalex.org/I4210088341"]},{"id":"https://openalex.org/I4210149618","display_name":"Guangdong University of Finance","ror":"https://ror.org/04grzdh47","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210149618"]}],"countries":["CN","MN"],"is_corresponding":true,"raw_author_name":"Yongyi Gu","raw_affiliation_strings":["School of Statistics and Mathematics, Guangdong, University of Finance and Economics, Guangzhou, 510320"],"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Guangdong, University of Finance and Economics, Guangzhou, 510320","institution_ids":["https://openalex.org/I201459984","https://openalex.org/I4210088341","https://openalex.org/I4210149618"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017483602","display_name":"Fanning Meng","orcid":"https://orcid.org/0000-0002-8239-9849"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fanning Meng","raw_affiliation_strings":["School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006","institution_ids":["https://openalex.org/I37987034"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017483602","https://openalex.org/A5084985048"],"corresponding_institution_ids":["https://openalex.org/I201459984","https://openalex.org/I37987034","https://openalex.org/I4210088341","https://openalex.org/I4210149618"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":5.1837,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.96383742,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"2019","issue":"1","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":1.0,"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":1.0,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/trigonometric-functions","display_name":"Trigonometric functions","score":0.7359017133712769},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.6696884632110596},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6625634431838989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6225787401199341},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.6071738004684448},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5608587265014648},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5473660230636597},{"id":"https://openalex.org/keywords/kadomtsev\u2013petviashvili-equation","display_name":"Kadomtsev\u2013Petviashvili equation","score":0.5069794654846191},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5009145736694336},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46828386187553406},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.428547739982605},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40109798312187195},{"id":"https://openalex.org/keywords/characteristic-equation","display_name":"Characteristic equation","score":0.3038465976715088},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2363491952419281},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09813538193702698},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.057795315980911255}],"concepts":[{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.7359017133712769},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.6696884632110596},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6625634431838989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6225787401199341},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.6071738004684448},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5608587265014648},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5473660230636597},{"id":"https://openalex.org/C159785203","wikidata":"https://www.wikidata.org/wiki/Q6345653","display_name":"Kadomtsev\u2013Petviashvili equation","level":4,"score":0.5069794654846191},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5009145736694336},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46828386187553406},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.428547739982605},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40109798312187195},{"id":"https://openalex.org/C53744967","wikidata":"https://www.wikidata.org/wiki/Q1062971","display_name":"Characteristic equation","level":3,"score":0.3038465976715088},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2363491952419281},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09813538193702698},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.057795315980911255},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/9314693","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/9314693","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/9314693.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:9314693","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/9314693.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:ae109f680ba14bb89617640eeaf24ca6","is_oa":true,"landing_page_url":"https://doaj.org/article/ae109f680ba14bb89617640eeaf24ca6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/9314693","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/9314693","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/9314693.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1016513002","display_name":null,"funder_award_id":"2016A030310257","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G108708396","display_name":null,"funder_award_id":"11701111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1477544716","display_name":null,"funder_award_id":"Guangdong","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2410353519","display_name":null,"funder_award_id":"11901111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3501998159","display_name":null,"funder_award_id":"2016A030310257","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8009906579","display_name":null,"funder_award_id":"1701111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2989827099.pdf","grobid_xml":"https://content.openalex.org/works/W2989827099.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W933054514","https://openalex.org/W964341284","https://openalex.org/W1968599836","https://openalex.org/W1982573234","https://openalex.org/W1983916790","https://openalex.org/W1995218400","https://openalex.org/W2002769487","https://openalex.org/W2007521282","https://openalex.org/W2014389907","https://openalex.org/W2026273364","https://openalex.org/W2027653567","https://openalex.org/W2044633502","https://openalex.org/W2044638725","https://openalex.org/W2076627362","https://openalex.org/W2080886039","https://openalex.org/W2088615732","https://openalex.org/W2094415343","https://openalex.org/W2122566989","https://openalex.org/W2147794691","https://openalex.org/W2164418115","https://openalex.org/W2183061247","https://openalex.org/W2329944935","https://openalex.org/W2402511393","https://openalex.org/W2485325947","https://openalex.org/W2504433158","https://openalex.org/W2586466339","https://openalex.org/W2603999474","https://openalex.org/W2728313399","https://openalex.org/W2736445013","https://openalex.org/W2748277091","https://openalex.org/W2766798264","https://openalex.org/W2767450776","https://openalex.org/W2773265440","https://openalex.org/W2779377105","https://openalex.org/W2790179491","https://openalex.org/W2795261949","https://openalex.org/W2796745387","https://openalex.org/W2807742183","https://openalex.org/W2809025181","https://openalex.org/W2887965685","https://openalex.org/W2888157777","https://openalex.org/W2889237467","https://openalex.org/W2891718102","https://openalex.org/W2902691728","https://openalex.org/W2910553078","https://openalex.org/W2912053916","https://openalex.org/W4213083888","https://openalex.org/W4232584877","https://openalex.org/W7067553488"],"related_works":["https://openalex.org/W4313655736","https://openalex.org/W3004912959","https://openalex.org/W3114797680","https://openalex.org/W2145456306","https://openalex.org/W2047182136","https://openalex.org/W2371773166","https://openalex.org/W4297795782","https://openalex.org/W4386850153","https://openalex.org/W4399563268","https://openalex.org/W2042873707"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,52],"derive":[4],"analytical":[5],"solutions":[6,27,39,61],"of":[7,28,47,62],"the":[8,19,29,45,54,63,71,81],"(2+1)\u2010dimensional":[9,64],"Kadomtsev\u2010Petviashvili":[10],"(KP)":[11],"equation":[12,31],"by":[13],"two":[14],"different":[15],"systematic":[16],"methods.":[17],"Using":[18],"exp\u2061(\u2212":[20],"\u03c8":[21],"(":[22],"z":[23],"))\u2010expansion":[24],"method,":[25],"exact":[26,60],"mentioned":[30],"including":[32],"hyperbolic,":[33],"exponential,":[34],"trigonometric,":[35],"and":[36,76],"rational":[37],"function":[38],"have":[40],"been":[41],"obtained.":[42],"Based":[43],"on":[44],"work":[46],"Yuan":[48],"et":[49],"al.":[50],",":[51],"proposed":[53],"extended":[55],"complex":[56,82],"method":[57],"to":[58,79],"seek":[59],"KP":[65],"equation.":[66],"The":[67],"results":[68],"demonstrate":[69],"that":[70],"applied":[72],"methods":[73,78],"are":[74],"efficient":[75],"direct":[77],"solve":[80],"nonlinear":[83],"systems.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":3}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}