{"id":"https://openalex.org/W3126267023","doi":"https://doi.org/10.3390/sym13020224","title":"Lie Group Method for Solving the Negative-Order Kadomtsev\u2013Petviashvili Equation (nKP)","display_name":"Lie Group Method for Solving the Negative-Order Kadomtsev\u2013Petviashvili Equation (nKP)","publication_year":2021,"publication_date":"2021-01-29","ids":{"openalex":"https://openalex.org/W3126267023","doi":"https://doi.org/10.3390/sym13020224","mag":"3126267023"},"language":"en","primary_location":{"id":"doi:10.3390/sym13020224","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13020224","pdf_url":"https://www.mdpi.com/2073-8994/13/2/224/pdf?version=1612701493","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/2/224/pdf?version=1612701493","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036086274","display_name":"Ghaylen Laouini","orcid":"https://orcid.org/0000-0002-6963-2482"},"institutions":[{"id":"https://openalex.org/I2803079837","display_name":"American University of the Middle East","ror":"https://ror.org/02gqgne03","country_code":"KW","type":"education","lineage":["https://openalex.org/I2803079837"]}],"countries":["KW"],"is_corresponding":false,"raw_author_name":"Ghaylen Laouini","raw_affiliation_strings":["College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait","institution_ids":["https://openalex.org/I2803079837"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005208424","display_name":"Amr M. Amin","orcid":"https://orcid.org/0000-0002-0175-6251"},"institutions":[{"id":"https://openalex.org/I80693520","display_name":"American University in Cairo","ror":"https://ror.org/0176yqn58","country_code":"EG","type":"education","lineage":["https://openalex.org/I80693520"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Amr M. Amin","raw_affiliation_strings":["School of Sciences and Engineering, The American University in Cairo, New Cairo 11835, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Sciences and Engineering, The American University in Cairo, New Cairo 11835, Egypt","institution_ids":["https://openalex.org/I80693520"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022815891","display_name":"Mohamed Moustafa","orcid":"https://orcid.org/0000-0001-8410-3354"},"institutions":[{"id":"https://openalex.org/I80693520","display_name":"American University in Cairo","ror":"https://ror.org/0176yqn58","country_code":"EG","type":"education","lineage":["https://openalex.org/I80693520"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Mohamed Moustafa","raw_affiliation_strings":["School of Sciences and Engineering, The American University in Cairo, New Cairo 11835, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Sciences and Engineering, The American University in Cairo, New Cairo 11835, Egypt","institution_ids":["https://openalex.org/I80693520"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005208424","https://openalex.org/A5022815891"],"corresponding_institution_ids":["https://openalex.org/I80693520"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.1597,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.76937174,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"13","issue":"2","first_page":"224","last_page":"224"},"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9861999750137329,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.98580002784729,"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/kadomtsev\u2013petviashvili-equation","display_name":"Kadomtsev\u2013Petviashvili equation","score":0.7729511857032776},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7375312447547913},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6274406313896179},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.584239661693573},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5093010663986206},{"id":"https://openalex.org/keywords/symmetry-group","display_name":"Symmetry group","score":0.5053539872169495},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.4920629858970642},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4904288947582245},{"id":"https://openalex.org/keywords/infinitesimal","display_name":"Infinitesimal","score":0.47101888060569763},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4581351578235626},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4300377368927002},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.42414572834968567},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.41747045516967773},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3711045980453491},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.371042937040329},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.296633780002594},{"id":"https://openalex.org/keywords/characteristic-equation","display_name":"Characteristic equation","score":0.21458274126052856},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16352158784866333},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12150153517723083},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09490993618965149}],"concepts":[{"id":"https://openalex.org/C159785203","wikidata":"https://www.wikidata.org/wiki/Q6345653","display_name":"Kadomtsev\u2013Petviashvili equation","level":4,"score":0.7729511857032776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7375312447547913},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6274406313896179},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.584239661693573},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5093010663986206},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.5053539872169495},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.4920629858970642},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4904288947582245},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.47101888060569763},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4581351578235626},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4300377368927002},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.42414572834968567},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.41747045516967773},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3711045980453491},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.371042937040329},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.296633780002594},{"id":"https://openalex.org/C53744967","wikidata":"https://www.wikidata.org/wiki/Q1062971","display_name":"Characteristic equation","level":3,"score":0.21458274126052856},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16352158784866333},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12150153517723083},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09490993618965149},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13020224","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13020224","pdf_url":"https://www.mdpi.com/2073-8994/13/2/224/pdf?version=1612701493","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a73463db49a84557aaf5e9de09c86442","is_oa":true,"landing_page_url":"https://doaj.org/article/a73463db49a84557aaf5e9de09c86442","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 2, p 224 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/2/224/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13020224","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 13; Issue 2; Pages: 224","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13020224","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13020224","pdf_url":"https://www.mdpi.com/2073-8994/13/2/224/pdf?version=1612701493","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3126267023.pdf","grobid_xml":"https://content.openalex.org/works/W3126267023.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W90800293","https://openalex.org/W1573927207","https://openalex.org/W1633315028","https://openalex.org/W1969428562","https://openalex.org/W1975657498","https://openalex.org/W1987881546","https://openalex.org/W1995735498","https://openalex.org/W1999017987","https://openalex.org/W2009823664","https://openalex.org/W2014630631","https://openalex.org/W2017358916","https://openalex.org/W2019025756","https://openalex.org/W2034796287","https://openalex.org/W2038057591","https://openalex.org/W2039677202","https://openalex.org/W2040474613","https://openalex.org/W2053833421","https://openalex.org/W2062572188","https://openalex.org/W2066493483","https://openalex.org/W2069428234","https://openalex.org/W2073817609","https://openalex.org/W2083960709","https://openalex.org/W2091442665","https://openalex.org/W2127965024","https://openalex.org/W2149557743","https://openalex.org/W2152119681","https://openalex.org/W2170587918","https://openalex.org/W2324210594","https://openalex.org/W2339719775","https://openalex.org/W2490894620","https://openalex.org/W2551504577","https://openalex.org/W2590362739","https://openalex.org/W2797256054","https://openalex.org/W4229672964","https://openalex.org/W4232650420","https://openalex.org/W4255732627","https://openalex.org/W6729716100"],"related_works":["https://openalex.org/W2010182028","https://openalex.org/W2999602081","https://openalex.org/W1512920608","https://openalex.org/W4401010376","https://openalex.org/W2023741689","https://openalex.org/W1990874070","https://openalex.org/W2351690041","https://openalex.org/W2049935045","https://openalex.org/W4297685110","https://openalex.org/W2348357475"],"abstract_inverted_index":{"A":[0],"comprehensive":[1],"study":[2],"of":[3],"the":[4,19,30,35,44,49,54,62,70,76,90],"negative-order":[5,36,55],"Kadomtsev\u2013Petviashvili":[6,37],"(nKP)":[7],"partial":[8],"differential":[9],"equation":[10,57],"by":[11,28],"Lie":[12,31],"group":[13,32],"method":[14,33,74,79],"has":[15],"been":[16,40,59],"presented.":[17],"Initially":[18],"infinitesimal":[20],"generators":[21],"and":[22,75,82,96],"symmetry":[23],"reduction,":[24],"which":[25],"were":[26],"obtained":[27],"applying":[29],"on":[34],"equation,":[38],"have":[39,58],"used":[41],"for":[42,53,89],"constructing":[43,85],"reduced":[45,63],"equations.":[46],"In":[47],"particular,":[48],"traveling":[50,91],"wave":[51,92],"solutions":[52,100],"KP":[56],"derived":[60],"from":[61],"equations":[64],"as":[65],"an":[66],"invariant":[67],"solution.":[68],"Finally,":[69],"extended":[71,77],"improved":[72],"(G\u2032/G)":[73],"tanh":[78],"are":[80,101],"described":[81],"applied":[83],"in":[84],"new":[86,95],"explicit":[87],"expressions":[88],"solutions.":[93],"Many":[94],"more":[97],"general":[98],"exact":[99],"obtained.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
