{"id":"https://openalex.org/W4410924443","doi":"https://doi.org/10.1155/cplx/2800207","title":"Novel Soliton and Wave Solutions for the Dual\u2010Perturbed Integrable Boussinesq Equation","display_name":"Novel Soliton and Wave Solutions for the Dual\u2010Perturbed Integrable Boussinesq Equation","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4410924443","doi":"https://doi.org/10.1155/cplx/2800207"},"language":"en","primary_location":{"id":"doi:10.1155/cplx/2800207","is_oa":true,"landing_page_url":"https://doi.org/10.1155/cplx/2800207","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cplx/2800207","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://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cplx/2800207","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034369096","display_name":"Akhtar Hussain","orcid":"https://orcid.org/0000-0002-1892-3212"},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]},{"id":"https://openalex.org/I172780181","display_name":"University of the Punjab","ror":"https://ror.org/011maz450","country_code":"PK","type":"education","lineage":["https://openalex.org/I172780181"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Akhtar Hussain","raw_affiliation_strings":["Department of Mathematics and Statistics ,  The University of Lahore ,  Lahore , Punjab,  Pakistan ,  uol.edu.pk"],"raw_orcid":"https://orcid.org/0000-0002-1892-3212","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics ,  The University of Lahore ,  Lahore , Punjab,  Pakistan ,  uol.edu.pk","institution_ids":["https://openalex.org/I172780181","https://openalex.org/I142204992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015130444","display_name":"Tarek F. Ibrahim","orcid":"https://orcid.org/0000-0002-6895-3268"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Tarek F. Ibrahim","raw_affiliation_strings":["Department of Mathematics ,  Sciences College ,  King Khalid University ,  Abha ,  Saudi Arabia ,  kku.edu.sa"],"raw_orcid":"https://orcid.org/0000-0002-6895-3268","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Sciences College ,  King Khalid University ,  Abha ,  Saudi Arabia ,  kku.edu.sa","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114495110","display_name":"Faizah D. Alanazi","orcid":null},"institutions":[{"id":"https://openalex.org/I118590987","display_name":"Northern Border University","ror":"https://ror.org/03j9tzj20","country_code":"SA","type":"education","lineage":["https://openalex.org/I118590987"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Faizah D. Alanazi","raw_affiliation_strings":["Department of Mathematics ,  College of Science ,  Northern Border University ,  Arar ,  Saudi Arabia ,  nbu.edu.sa"],"raw_orcid":"https://orcid.org/0009-0002-3622-1238","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  College of Science ,  Northern Border University ,  Arar ,  Saudi Arabia ,  nbu.edu.sa","institution_ids":["https://openalex.org/I118590987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087807152","display_name":"Waleed M. Osman","orcid":null},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Waleed M. Osman","raw_affiliation_strings":["Department of Mathematics ,  Applied College at Dhahran Al Janoub ,  King Khalid University ,  Abha ,  62529 ,  Saudi Arabia ,  kku.edu.sa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Applied College at Dhahran Al Janoub ,  King Khalid University ,  Abha ,  62529 ,  Saudi Arabia ,  kku.edu.sa","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032898411","display_name":"Arafa A. Dawood","orcid":null},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Arafa A. Dawood","raw_affiliation_strings":["Department of Human Resources Management ,  College of Business ,  King Khalid University ,  Abha ,  Saudi Arabia ,  kku.edu.sa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Human Resources Management ,  College of Business ,  King Khalid University ,  Abha ,  Saudi Arabia ,  kku.edu.sa","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036867612","display_name":"Jorge Herrera","orcid":"https://orcid.org/0000-0003-0273-4043"},"institutions":[{"id":"https://openalex.org/I231847692","display_name":"Universidad de Bogot\u00e1 Jorge Tadeo Lozano","ror":"https://ror.org/04wbzgn90","country_code":"CO","type":"education","lineage":["https://openalex.org/I231847692"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Jorge Herrera","raw_affiliation_strings":["Facultad de Ciencias Naturales e Ingenieria ,  Universidad de Bogota Jorge Tadeo Lozano ,  Bogota ,  110311 ,  Colombia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Ciencias Naturales e Ingenieria ,  Universidad de Bogota Jorge Tadeo Lozano ,  Bogota ,  110311 ,  Colombia","institution_ids":["https://openalex.org/I231847692"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5034369096"],"corresponding_institution_ids":["https://openalex.org/I142204992","https://openalex.org/I172780181"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":2.2657,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.87634216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"2025","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":0.9995999932289124,"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":0.9995999932289124,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9952999949455261,"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/integrable-system","display_name":"Integrable system","score":0.8150925636291504},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.6603043675422668},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.6031296849250793},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.52289217710495},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4778011441230774},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4737580418586731},{"id":"https://openalex.org/keywords/periodic-wave","display_name":"Periodic wave","score":0.46358394622802734},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.44285014271736145},{"id":"https://openalex.org/keywords/boussinesq-approximation","display_name":"Boussinesq approximation (buoyancy)","score":0.4139684736728668},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.4098132252693176},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32696259021759033},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1301497220993042},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1077377200126648},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10343468189239502},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.051524847745895386},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.04763433337211609}],"concepts":[{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.8150925636291504},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.6603043675422668},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6031296849250793},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.52289217710495},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4778011441230774},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4737580418586731},{"id":"https://openalex.org/C2993172089","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Periodic wave","level":3,"score":0.46358394622802734},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.44285014271736145},{"id":"https://openalex.org/C181152433","wikidata":"https://www.wikidata.org/wiki/Q895274","display_name":"Boussinesq approximation (buoyancy)","level":5,"score":0.4139684736728668},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.4098132252693176},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32696259021759033},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1301497220993042},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1077377200126648},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10343468189239502},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.051524847745895386},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.04763433337211609},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.0},{"id":"https://openalex.org/C106836276","wikidata":"https://www.wikidata.org/wiki/Q898249","display_name":"Rayleigh number","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/cplx/2800207","is_oa":true,"landing_page_url":"https://doi.org/10.1155/cplx/2800207","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cplx/2800207","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:doaj.org/article:75b47a1a76c84e9bb1251a92fdf9e82d","is_oa":true,"landing_page_url":"https://doaj.org/article/75b47a1a76c84e9bb1251a92fdf9e82d","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":"Complexity, Vol 2025 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/cplx/2800207","is_oa":true,"landing_page_url":"https://doi.org/10.1155/cplx/2800207","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cplx/2800207","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/G1983314458","display_name":null,"funder_award_id":"RGP2/55/46","funder_id":"https://openalex.org/F4320324433","funder_display_name":"King Khalid University"},{"id":"https://openalex.org/G8197534824","display_name":null,"funder_award_id":"NBU-FFR-2025-1102-08","funder_id":"https://openalex.org/F4320328654","funder_display_name":"Northern Border University"}],"funders":[{"id":"https://openalex.org/F4320324433","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30"},{"id":"https://openalex.org/F4320328654","display_name":"Northern Border University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410924443.pdf","grobid_xml":"https://content.openalex.org/works/W4410924443.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1505625590","https://openalex.org/W1993190416","https://openalex.org/W2011797779","https://openalex.org/W2013528121","https://openalex.org/W2027588087","https://openalex.org/W2047779330","https://openalex.org/W2048920804","https://openalex.org/W2054602473","https://openalex.org/W2080451582","https://openalex.org/W2084640917","https://openalex.org/W2086698446","https://openalex.org/W2089364815","https://openalex.org/W2094892214","https://openalex.org/W2132478094","https://openalex.org/W2163318888","https://openalex.org/W2317745818","https://openalex.org/W2408822706","https://openalex.org/W2547309506","https://openalex.org/W2769243249","https://openalex.org/W2783405586","https://openalex.org/W3016532901","https://openalex.org/W3040252065","https://openalex.org/W3195180976","https://openalex.org/W4239578847","https://openalex.org/W4281727788","https://openalex.org/W4318995032","https://openalex.org/W4319264857","https://openalex.org/W4366593975","https://openalex.org/W4386495207","https://openalex.org/W4386803398","https://openalex.org/W4390457183","https://openalex.org/W4390877624","https://openalex.org/W4402420604","https://openalex.org/W4403445928","https://openalex.org/W4404929663","https://openalex.org/W4405043664","https://openalex.org/W4406998460"],"related_works":["https://openalex.org/W1968454318","https://openalex.org/W2277269733","https://openalex.org/W2682605843","https://openalex.org/W4286504938","https://openalex.org/W2363658832","https://openalex.org/W2086924551","https://openalex.org/W2792677503","https://openalex.org/W2030436219","https://openalex.org/W2369768928","https://openalex.org/W2382007108"],"abstract_inverted_index":{"Nonlinear":[0],"science":[1],"represents":[2],"a":[3],"foundational":[4],"frontier":[5],"in":[6,15,115],"scientific":[7],"inquiry":[8],"that":[9,109],"explores":[10],"the":[11,22,37,44,53,91,94,116,129],"shared":[12],"characteristics":[13],"inherent":[14,132],"nonlinear":[16,59],"phenomena.":[17],"This":[18],"study":[19],"focused":[20],"on":[21],"perturbed":[23],"Boussinesq":[24],"(PB)":[25],"equation":[26],"incorporating":[27],"dual":[28],"perturbation":[29],"terms.":[30],"Soliton":[31],"solutions":[32,102],"were":[33,80,124],"deduced":[34],"by":[35,42],"leveraging":[36],"traveling":[38],"wave":[39,60,98],"hypothesis.":[40],"Furthermore,":[41],"employing":[43],"generalized":[45],"Jacobi":[46],"elliptic":[47],"expansion":[48],"function":[49],"(JEEF)":[50],"method":[51],"and":[52,76,105,121],"improved":[54],"tan":[55],"(\u039b/2)":[56],"method,":[57],"diverse":[58],"solutions,":[61,79],"including":[62],"kink,":[63],"dark,":[64],"periodic,":[65],"bright,":[66],"singular,":[67],"periodic":[68],"waves,":[69,73,75],"bell\u2010shaped":[70],"solitons,":[71],"solitary":[72],"shock":[74],"kink\u2010shaped":[77],"soliton":[78],"acquired.":[81],"The":[82],"establishment":[83],"of":[84,96],"constraint":[85],"relations":[86],"is":[87],"detailed":[88],"to":[89,126,133],"delineate":[90],"criteria":[92],"for":[93],"existence":[95],"these":[97,101,134],"solutions.":[99,138],"Notably,":[100],"are":[103],"innovative":[104],"present":[106],"novel":[107],"contributions":[108],"have":[110],"not":[111],"yet":[112],"been":[113],"documented":[114],"literature.":[117],"In":[118],"addition,":[119],"2D":[120],"3D":[122],"graphics":[123],"constructed":[125],"visually":[127],"elucidate":[128],"physical":[130],"behavior":[131],"newly":[135],"acquired":[136],"exact":[137]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
