{"id":"https://openalex.org/W7225643204","doi":"https://doi.org/10.3390/math14214095","title":"Explicit Non-Traveling Wave Solutions for the (3 1)-Dimensional Nonlinear Vakhnenko\u2013Parkes Equation Arising in Fluid Dynamics+","display_name":"Explicit Non-Traveling Wave Solutions for the (3 1)-Dimensional Nonlinear Vakhnenko\u2013Parkes Equation Arising in Fluid Dynamics+","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225643204","doi":"https://doi.org/10.3390/math14214095"},"language":"en","primary_location":{"id":"doi:10.3390/math14214095","doi":"https://doi.org/10.3390/math14214095","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14214095","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/math14214095","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037073575","display_name":"Shami A. M. Alsallami","orcid":"https://orcid.org/0000-0001-5480-9866","observed_orcids":["https://orcid.org/0000-0001-5480-9866"]},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Shami A. M. Alsallami","raw_affiliation_strings":["Mathematics Department, College of Sciences, Umm Al-Qura University, Makkah 24381, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5480-9866","affiliations":[{"raw_affiliation_string":"Mathematics Department, College of Sciences, Umm Al-Qura University, Makkah 24381, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037073575"],"corresponding_institution_ids":["https://openalex.org/I199693650"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"21","first_page":"4095","last_page":"4095"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/3-1-dimensional-nonlinear-evolution-equation","display_name":"(3+1)-dimensional nonlinear evolution equation","score":0.8989999890327454},{"id":"https://openalex.org/keywords/exact-solutions","display_name":"exact solutions","score":0.9290000200271606},{"id":"https://openalex.org/keywords/arbitrary-functions","display_name":"arbitrary functions","score":0.8180000185966492},{"id":"https://openalex.org/keywords/jacobi-elliptic-functions","display_name":"Jacobi elliptic functions","score":0.8270000219345093},{"id":"https://openalex.org/keywords/variable-coefficient-nonlinear-evolution-equations","display_name":"variable-coefficient nonlinear evolution equations","score":0.7699999809265137},{"id":"https://openalex.org/keywords/fluid-dynamics","display_name":"fluid dynamics","score":0.847000002861023}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.677299976348877},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6651999950408936},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6366999745368958},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6222000122070312},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5146999955177307},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4814999997615814},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45339998602867126},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3917999863624573},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.3361999988555908},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.28700000047683716},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.28299999237060547},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C2780091087","wikidata":"https://www.wikidata.org/wiki/Q3092131","display_name":"Dimensional reduction","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/math14214095","doi":"https://doi.org/10.3390/math14214095","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14214095","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/math14214095","doi":"https://doi.org/10.3390/math14214095","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14214095","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3015393383","https://openalex.org/W2069789481","https://openalex.org/W4411142511","https://openalex.org/W2080886039","https://openalex.org/W7167905699","https://openalex.org/W4220676447","https://openalex.org/W2283709800","https://openalex.org/W2019176245","https://openalex.org/W2017910626","https://openalex.org/W4396860328"],"abstract_inverted_index":{"The":[0,81,157,185,199],"present":[1],"work":[2],"aims":[3],"to":[4,10,124,177],"utilize":[5],"two":[6],"extended":[7],"reduction":[8,46,158],"strategies":[9,159],"the":[11,27,45,49,60,85,107,111,115,122,136,179,182,196],"(3+1)\u2013dimensional":[12],"nonlinear":[13,154,211],"Vakhnenko\u2013Parkes":[14],"equation":[15,29,51],"and":[16,67,101,144,151],"construct":[17],"some":[18],"novel":[19],"exact":[20,165,205],"non-traveling":[21,204],"wave":[22,103,142,155],"solutions.":[23,184],"These":[24],"approaches":[25],"transform":[26],"main":[28,108],"into":[30,195],"several":[31,162,174],"solvable":[32],"reduced":[33,50,58],"equations.":[34],"In":[35],"each":[36],"strategy,":[37],"we":[38],"first":[39],"isolate":[40],"an":[41,55],"unconstrained":[42],"regime":[43],"of":[44,77,106,110,117,149,164,181,187],"in":[47,90,128,132],"which":[48,120],"holds":[52],"identically":[53],"for":[54,207],"arbitrary":[56,118],"smooth":[57],"function;":[59],"exponential,":[61,95],"trigonometric,":[62,96],"hyperbolic,":[63,97],"rational,":[64,98],"Jacobi":[65,99],"elliptic,":[66,100],"hybrid":[68,102],"solution":[69],"types":[70],"are":[71,88],"then":[72],"obtained":[73,83],"as":[74],"particular":[75],"choices":[76],"this":[78],"general":[79],"family.":[80],"solutions":[82,113,123,138,143,166,189,206],"from":[84],"proposed":[86,200],"techniques":[87],"expressed":[89],"generalized":[91],"forms":[92],"that":[93],"combine":[94],"structures.":[104],"One":[105],"properties":[109],"constructed":[112],"is":[114,190],"presence":[116],"functions,":[119],"allows":[121],"possess":[125],"greater":[126],"flexibility":[127],"describing":[129],"various":[130],"phenomena":[131],"practical":[133],"applications.":[134],"Consequently,":[135],"resulting":[137],"generalize":[139],"conventional":[140],"traveling":[141],"provide":[145],"a":[146],"flexible":[147],"description":[148],"non-autonomous":[150],"spatially":[152],"modulated":[153],"patterns.":[156],"employed":[160],"generate":[161],"families":[163],"with":[167],"diverse":[168,215],"functional":[169],"forms.":[170],"We":[171],"subsequently":[172],"include":[173],"graphical":[175],"representations":[176],"illustrate":[178],"shape":[180],"given":[183],"correctness":[186],"all":[188],"verified":[191],"by":[192],"direct":[193],"substitution":[194],"governing":[197],"equation.":[198],"framework":[201],"systematically":[202],"constructs":[203],"higher-dimensional":[208],"or":[209],"variable-coefficient":[210],"evolution":[212],"equations":[213],"across":[214],"physical":[216],"fields.":[217]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
