{"id":"https://openalex.org/W4404525035","doi":"https://doi.org/10.3390/fractalfract8110672","title":"Investigating the Dynamics of a Unidirectional Wave Model: Soliton Solutions, Bifurcation, and Chaos Analysis","display_name":"Investigating the Dynamics of a Unidirectional Wave Model: Soliton Solutions, Bifurcation, and Chaos Analysis","publication_year":2024,"publication_date":"2024-11-18","ids":{"openalex":"https://openalex.org/W4404525035","doi":"https://doi.org/10.3390/fractalfract8110672"},"language":"en","primary_location":{"id":"doi:10.3390/fractalfract8110672","doi":"https://doi.org/10.3390/fractalfract8110672","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract8110672","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1"],"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":"Fractal and Fractional","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/fractalfract8110672","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013716670","display_name":"Tariq Alraqad","orcid":"https://orcid.org/0000-0002-8881-4812","observed_orcids":["https://orcid.org/0000-0002-8881-4812"]},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Tariq Alraqad","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 55473, Saudi Arabia","Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 55473, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104067121","display_name":"Muntasir Suhail","orcid":"https://orcid.org/0009-0009-6835-4896","observed_orcids":["https://orcid.org/0009-0009-6835-4896"]},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Muntasir Suhail","raw_affiliation_strings":["Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000154542","display_name":"Hicham Saber","orcid":"https://orcid.org/0000-0003-3453-9277","observed_orcids":["https://orcid.org/0000-0003-3453-9277"]},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Hicham Saber","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 55473, Saudi Arabia","Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 55473, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066453993","display_name":"Khaled Aldwoah","orcid":"https://orcid.org/0000-0001-5731-3532","observed_orcids":["https://orcid.org/0000-0001-5731-3532"]},"institutions":[{"id":"https://openalex.org/I4210151290","display_name":"Islamic University of Madinah","ror":"https://ror.org/03rcp1y74","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210151290"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Khaled Aldwoah","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5731-3532","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia","institution_ids":["https://openalex.org/I4210151290"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089077674","display_name":"Nidal H. E. Eljaneid","orcid":"https://orcid.org/0009-0001-9664-9351","observed_orcids":["https://orcid.org/0009-0001-9664-9351"]},"institutions":[{"id":"https://openalex.org/I72264486","display_name":"University of Tabuk","ror":"https://ror.org/04yej8x59","country_code":"SA","type":"education","lineage":["https://openalex.org/I72264486"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Nidal Eljaneid","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia","institution_ids":["https://openalex.org/I72264486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018823211","display_name":"Amer Alsulami","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Amer Alsulami","raw_affiliation_strings":["Department of Mathematics, Turabah University College, Taif University, Taif 21944, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Turabah University College, Taif University, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114712049","display_name":"Blgys Muflh","orcid":"https://orcid.org/0009-0008-0679-6413","observed_orcids":["https://orcid.org/0009-0008-0679-6413"]},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Blgys Muflh","raw_affiliation_strings":["Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5066453993","https://openalex.org/A5104067121"],"corresponding_institution_ids":["https://openalex.org/I156216236","https://openalex.org/I4210151290"],"apc_list":{"value":2700,"currency":"CHF","value_usd":3069},"apc_paid":{"value":2700,"currency":"CHF","value_usd":3069},"fwci":0.7605,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.67435822,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"8","issue":"11","first_page":"672","last_page":"672"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9970999956130981,"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":0.9970999956130981,"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":0.0017000000225380063,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/soliton-solutions","display_name":"soliton solutions","score":0.9610000252723694},{"id":"https://openalex.org/keywords/bifurcation-analysis","display_name":"bifurcation analysis","score":0.8550000190734863},{"id":"https://openalex.org/keywords/chaos","display_name":"chaos","score":0.6880000233650208},{"id":"https://openalex.org/keywords/sensitivity-analysis","display_name":"sensitivity analysis","score":0.9079999923706055},{"id":"https://openalex.org/keywords/fractional-order-systems","display_name":"fractional-order systems","score":0.7720000147819519},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"quantum mechanics","score":0.5239999890327454},{"id":"https://openalex.org/keywords/phase-plane-analysis","display_name":"phase plane analysis","score":0.7670000195503235},{"id":"https://openalex.org/keywords/nonlinear-evolution-equations","display_name":"nonlinear evolution equations","score":0.6370000243186951}],"concepts":[{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.7681477069854736},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7463053464889526},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5671578645706177},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4817759692668915},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.47698909044265747},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4744777977466583},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.4720229506492615},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4123159348964691},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.39190244674682617},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.3122987151145935},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24548348784446716},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22029656171798706},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.06982368230819702},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06718188524246216},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/fractalfract8110672","doi":"https://doi.org/10.3390/fractalfract8110672","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract8110672","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1"],"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":"Fractal and Fractional","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:20f7cdd5084b4043bf375050726614d7","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/20f7cdd5084b4043bf375050726614d7","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,"listed_in":[],"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":"Fractal and Fractional, Vol 8, Iss 11, p 672 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/fractalfract8110672","doi":"https://doi.org/10.3390/fractalfract8110672","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract8110672","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1"],"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":"Fractal and Fractional","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5120360896","display_name":null,"funder_award_id":"QU-APC-2024-9/1","funder_id":"https://openalex.org/F4320324403","funder_display_name":"Qassim University"}],"funders":[{"id":"https://openalex.org/F4320324403","display_name":"Qassim University","ror":"https://ror.org/01wsfe280"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1631607997","https://openalex.org/W1984853762","https://openalex.org/W2021174376","https://openalex.org/W3044135167","https://openalex.org/W3087136512","https://openalex.org/W3098546160","https://openalex.org/W3200685977","https://openalex.org/W4226213671","https://openalex.org/W4296449273","https://openalex.org/W4309048288","https://openalex.org/W4309670911","https://openalex.org/W4319264857","https://openalex.org/W4319871808","https://openalex.org/W4323664231","https://openalex.org/W4376616848","https://openalex.org/W4385704422","https://openalex.org/W4389204799","https://openalex.org/W4389940057","https://openalex.org/W4390245612","https://openalex.org/W4390638739","https://openalex.org/W4390663651","https://openalex.org/W4391295811","https://openalex.org/W4391530044","https://openalex.org/W4391986493","https://openalex.org/W4392508365","https://openalex.org/W4392648783","https://openalex.org/W4392728095","https://openalex.org/W4392761065","https://openalex.org/W4399068632","https://openalex.org/W4401664906","https://openalex.org/W4401894121","https://openalex.org/W4402728288","https://openalex.org/W4403157767","https://openalex.org/W4403247763","https://openalex.org/W4403588240","https://openalex.org/W4403982981"],"related_works":["https://openalex.org/W2014696479","https://openalex.org/W2060450020","https://openalex.org/W2095274406","https://openalex.org/W2271295025","https://openalex.org/W4321135758","https://openalex.org/W1898914577","https://openalex.org/W2167230766","https://openalex.org/W1983047697","https://openalex.org/W139684681","https://openalex.org/W2513783521"],"abstract_inverted_index":{"The":[0,132],"current":[1],"work":[2],"investigates":[3],"a":[4,30,69,104],"recently":[5],"introduced":[6],"unidirectional":[7],"wave":[8,154],"model,":[9],"applicable":[10],"in":[11,39,139,144,164,169],"science":[12],"and":[13,19,64,99,125,156,171],"engineering":[14,170],"to":[15,42,81],"understand":[16],"complex":[17,54,141],"systems":[18],"phenomena.":[20],"This":[21,159],"investigation":[22],"has":[23],"two":[24],"primary":[25],"aims.":[26],"First,":[27],"it":[28,51],"employs":[29],"novel":[31],"modified":[32],"Sardar":[33],"sub-equation":[34],"method,":[35,122],"not":[36],"yet":[37],"explored":[38],"the":[40,47,53,58,74,83,87,91,95,117,120,166],"literature,":[41],"derive":[43],"new":[44],"solutions":[45,127,135],"for":[46],"governing":[48,59],"model.":[49],"Second,":[50],"analyzes":[52],"dynamical":[55],"structure":[56],"of":[57,73,86,94,119],"model":[60],"using":[61,110],"bifurcation,":[62],"chaos,":[63],"sensitivity":[65],"analyses.":[66],"To":[67,89],"provide":[68],"more":[70],"accurate":[71],"depiction":[72],"underlying":[75],"dynamics,":[76,150],"they":[77],"use":[78],"quantum":[79],"mechanics":[80],"explain":[82],"intricate":[84],"behavior":[85,93],"system.":[88],"illustrate":[90],"physical":[92,142],"obtained":[96],"solutions,":[97],"2D":[98],"3D":[100],"plots,":[101],"along":[102],"with":[103,128],"phase":[105],"plane":[106],"analysis,":[107],"are":[108],"presented":[109],"appropriate":[111],"parameter":[112],"values.":[113],"These":[114],"results":[115],"validate":[116],"effectiveness":[118],"employed":[121],"providing":[123],"thorough":[124],"consistent":[126],"significant":[129],"computational":[130],"efficiency.":[131],"investigated":[133],"soliton":[134,153],"will":[136],"be":[137],"valuable":[138],"understanding":[140],"structures":[143],"various":[145],"scientific":[146],"fields,":[147],"including":[148],"ferromagnetic":[149],"nonlinear":[151],"optics,":[152],"theory,":[155],"fiber":[157],"optics.":[158],"approach":[160],"proves":[161],"highly":[162],"effective":[163],"handling":[165],"complexities":[167],"inherent":[168],"mathematical":[172],"problems,":[173],"especially":[174],"those":[175],"involving":[176],"fractional-order":[177],"systems.":[178]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3}],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2025-10-10T00:00:00"}