{"id":"https://openalex.org/W4206502701","doi":"https://doi.org/10.3390/sym14020197","title":"New Localized and Periodic Solutions to a Korteweg\u2013de Vries Equation with Power Law Nonlinearity: Applications to Some Plasma Models","display_name":"New Localized and Periodic Solutions to a Korteweg\u2013de Vries Equation with Power Law Nonlinearity: Applications to Some Plasma Models","publication_year":2022,"publication_date":"2022-01-20","ids":{"openalex":"https://openalex.org/W4206502701","doi":"https://doi.org/10.3390/sym14020197"},"language":"en","primary_location":{"id":"doi:10.3390/sym14020197","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020197","pdf_url":"https://www.mdpi.com/2073-8994/14/2/197/pdf?version=1642734727","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/2073-8994/14/2/197/pdf?version=1642734727","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023575962","display_name":"S. A. El-Tantawy","orcid":"https://orcid.org/0000-0002-6724-7361"},"institutions":[{"id":"https://openalex.org/I88017793","display_name":"Port Said University","ror":"https://ror.org/01vx5yq44","country_code":"EG","type":"education","lineage":["https://openalex.org/I88017793"]},{"id":"https://openalex.org/I52207611","display_name":"Al Baha University","ror":"https://ror.org/0403jak37","country_code":"SA","type":"education","lineage":["https://openalex.org/I52207611"]}],"countries":["EG","SA"],"is_corresponding":true,"raw_author_name":"Samir A. El-Tantawy","raw_affiliation_strings":["Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt","Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Al Bahah 65731, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt","institution_ids":["https://openalex.org/I88017793"]},{"raw_affiliation_string":"Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Al Bahah 65731, Saudi Arabia","institution_ids":["https://openalex.org/I52207611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001448355","display_name":"Alvaro H. Salas","orcid":"https://orcid.org/0000-0001-9343-6062"},"institutions":[{"id":"https://openalex.org/I36243813","display_name":"Universidad Nacional de Colombia","ror":"https://ror.org/059yx9a68","country_code":"CO","type":"education","lineage":["https://openalex.org/I36243813"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Alvaro H. Salas","raw_affiliation_strings":["FIZMAKO Research Group, Department of Mathematics and Statistics, Universidad Nacional de Colombia, Bogota Cra 45, Colombia"],"affiliations":[{"raw_affiliation_string":"FIZMAKO Research Group, Department of Mathematics and Statistics, Universidad Nacional de Colombia, Bogota Cra 45, Colombia","institution_ids":["https://openalex.org/I36243813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073214349","display_name":"Wedad Albalawi","orcid":"https://orcid.org/0000-0002-9667-3933"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Wedad Albalawi","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11564, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11564, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023575962"],"corresponding_institution_ids":["https://openalex.org/I52207611","https://openalex.org/I88017793"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.253,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.87873788,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"14","issue":"2","first_page":"197","last_page":"197"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"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":0.9998999834060669,"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/T11603","display_name":"Dust and Plasma Wave Phenomena","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.9937999844551086,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.884023904800415},{"id":"https://openalex.org/keywords/ansatz","display_name":"Ansatz","score":0.6943129897117615},{"id":"https://openalex.org/keywords/cnoidal-wave","display_name":"Cnoidal wave","score":0.6548513770103455},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6081182360649109},{"id":"https://openalex.org/keywords/elliptic-function","display_name":"Elliptic function","score":0.5848661661148071},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4928781986236572},{"id":"https://openalex.org/keywords/jacobi-elliptic-functions","display_name":"Jacobi elliptic functions","score":0.4403214454650879},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43459415435791016},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4292908310890198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4032632112503052},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3477782905101776},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17451852560043335}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.884023904800415},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.6943129897117615},{"id":"https://openalex.org/C156470440","wikidata":"https://www.wikidata.org/wiki/Q5137392","display_name":"Cnoidal wave","level":3,"score":0.6548513770103455},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6081182360649109},{"id":"https://openalex.org/C123958593","wikidata":"https://www.wikidata.org/wiki/Q938102","display_name":"Elliptic function","level":2,"score":0.5848661661148071},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4928781986236572},{"id":"https://openalex.org/C73749972","wikidata":"https://www.wikidata.org/wiki/Q1473526","display_name":"Jacobi elliptic functions","level":2,"score":0.4403214454650879},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43459415435791016},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4292908310890198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4032632112503052},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3477782905101776},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17451852560043335}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14020197","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020197","pdf_url":"https://www.mdpi.com/2073-8994/14/2/197/pdf?version=1642734727","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:f2552571dbb24caabb7b9f8c9622005a","is_oa":true,"landing_page_url":"https://doaj.org/article/f2552571dbb24caabb7b9f8c9622005a","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 2, p 197 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/2/197/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14020197","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14020197","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020197","pdf_url":"https://www.mdpi.com/2073-8994/14/2/197/pdf?version=1642734727","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":[{"display_name":"Peace, Justice and strong institutions","score":0.8100000023841858,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1122018772","display_name":null,"funder_award_id":"PNURSP2022R157","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"},{"id":"https://openalex.org/G1787944550","display_name":null,"funder_award_id":"PNURSP2022R15","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"},{"id":"https://openalex.org/G2053653470","display_name":null,"funder_award_id":"PNURSP","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"},{"id":"https://openalex.org/G2893605509","display_name":null,"funder_award_id":"Saudi Arabia.","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"},{"id":"https://openalex.org/G4010074732","display_name":null,"funder_award_id":"Riyadh","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"},{"id":"https://openalex.org/G7606340142","display_name":null,"funder_award_id":"PNURSP2022R1","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"},{"id":"https://openalex.org/G8204392757","display_name":null,"funder_award_id":"PNURSP2022R","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"}],"funders":[{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4206502701.pdf","grobid_xml":"https://content.openalex.org/works/W4206502701.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W1531515307","https://openalex.org/W1633315028","https://openalex.org/W1969611818","https://openalex.org/W1970004836","https://openalex.org/W1973494951","https://openalex.org/W1976036779","https://openalex.org/W1976801708","https://openalex.org/W1978170327","https://openalex.org/W1991631175","https://openalex.org/W1992871943","https://openalex.org/W1996001214","https://openalex.org/W2001220107","https://openalex.org/W2003919201","https://openalex.org/W2020666255","https://openalex.org/W2024127151","https://openalex.org/W2035249396","https://openalex.org/W2045921433","https://openalex.org/W2049162834","https://openalex.org/W2081267519","https://openalex.org/W2081450017","https://openalex.org/W2087794091","https://openalex.org/W2089446317","https://openalex.org/W2094070000","https://openalex.org/W2094295163","https://openalex.org/W2122634014","https://openalex.org/W2137242086","https://openalex.org/W2141407049","https://openalex.org/W2164086069","https://openalex.org/W2327483094","https://openalex.org/W2337888165","https://openalex.org/W2548273632","https://openalex.org/W2892181390","https://openalex.org/W2920252964","https://openalex.org/W2962903164","https://openalex.org/W2968835675","https://openalex.org/W2980053426","https://openalex.org/W3019839372","https://openalex.org/W3098391201","https://openalex.org/W3126329694","https://openalex.org/W3134538625","https://openalex.org/W3153212173","https://openalex.org/W3153986985","https://openalex.org/W3157522081","https://openalex.org/W3197914891","https://openalex.org/W3204275631","https://openalex.org/W4243663477","https://openalex.org/W6652625808","https://openalex.org/W6672680266"],"related_works":["https://openalex.org/W4200576900","https://openalex.org/W2018226674","https://openalex.org/W1981598386","https://openalex.org/W2088931956","https://openalex.org/W4245335431","https://openalex.org/W2079666300","https://openalex.org/W2337781184","https://openalex.org/W2460717145","https://openalex.org/W2727005920","https://openalex.org/W2055501025"],"abstract_inverted_index":{"Traveling":[0],"wave":[1,41,73,93,101,160,177],"solutions,":[2,42],"including":[3],"localized":[4,40],"and":[5,13,25,136,183,217],"periodic":[6,14,159],"structures":[7],"(e.g.,":[8],"solitary":[9,44,72,92,100],"waves,":[10,12,45],"cnoidal":[11,176],"waves),":[15],"to":[16,46,69,88,103,162,179,193],"a":[17,90,109],"symmetry":[18],"Korteweg\u2013de":[19],"Vries":[20],"equation":[21,117,125,132],"(KdV)":[22],"with":[23,64,82,108,118,126,133,143],"integer":[24],"rational":[26],"power":[27,110],"law":[28,111],"nonlinearity":[29],"are":[30,53,67,86,153,186],"reported":[31],"using":[32],"several":[33,198],"approaches.":[34],"In":[35,58,75],"the":[36,39,47,59,76,79,99,115,121,129,148,163,168,175,180,195],"case":[37],"of":[38,170,197,204],"i.e.,":[43],"evolution":[48,164],"equation,":[49],"two":[50,140,144],"different":[51,141,145,202],"methods":[52],"devoted":[54],"for":[55,147,155],"this":[56],"purpose.":[57],"first":[60],"one,":[61,78],"new":[62],"hypotheses":[63],"Cole\u2013Hopf":[65],"transformation":[66],"employed":[68],"find":[70],"general":[71,91,158],"solutions.":[74],"second":[77],"ansatz":[80],"method":[81],"hyperbolic":[83],"sech":[84],"algorithm":[85],"utilized":[87],"obtain":[89],"solution.":[94],"The":[95],"obtained":[96],"solutions":[97,102,161,178],"recover":[98],"all":[104],"one-dimensional":[105],"KdV":[106,116,123,131],"equations":[107,185],"nonlinearity,":[112,120,128,135],"such":[113,206],"as":[114,207],"quadratic":[119],"modified":[122],"(mKdV)":[124],"cubic":[127],"super":[130],"quartic":[134],"so":[137,218],"on.":[138,219],"Furthermore,":[139],"approaches":[142],"formulas":[146],"Weierstrass":[149],"elliptic":[150,172],"functions":[151,173],"(WSEFs)":[152],"adopted":[154],"deriving":[156],"some":[157],"equation.":[165],"Additionally,":[166],"in":[167,201],"form":[169],"Jacobi":[171],"(JEFs),":[174],"KdV-,":[181],"mKdV-,":[182],"SKdV":[184],"obtained.":[187],"These":[188],"results":[189],"help":[190],"many":[191],"authors":[192],"understand":[194],"mystery":[196],"nonlinear":[199,212],"phenomena":[200],"branches":[203],"sciences,":[205],"plasma":[208],"physics,":[209],"fluid":[210],"mechanics,":[211],"optics,":[213],"Bose":[214],"Einstein":[215],"condensates,":[216]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":9}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2022-01-25T00:00:00"}
