{"id":"https://openalex.org/W4413127879","doi":"https://doi.org/10.3390/axioms14080624","title":"Analytical Solutions for Generalized Stochastic HSC-KdV Equations with Variable Coefficients Using Hermite Transform and F-Expansion Method","display_name":"Analytical Solutions for Generalized Stochastic HSC-KdV Equations with Variable Coefficients Using Hermite Transform and F-Expansion Method","publication_year":2025,"publication_date":"2025-08-10","ids":{"openalex":"https://openalex.org/W4413127879","doi":"https://doi.org/10.3390/axioms14080624"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14080624","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080624","pdf_url":"https://www.mdpi.com/2075-1680/14/8/624/pdf?version=1755058653","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/8/624/pdf?version=1755058653","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060547119","display_name":"Mohammed Zakarya","orcid":"https://orcid.org/0000-0003-4312-8330"},"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":"Mohammed Zakarya","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-4312-8330","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004499466","display_name":"Nadiah Zafer Al-Shehri","orcid":"https://orcid.org/0009-0001-7968-4913"},"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":"Nadiah Zafer Al-Shehri","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082512122","display_name":"Hegagi Mohamed Ali","orcid":"https://orcid.org/0000-0003-0159-6726"},"institutions":[{"id":"https://openalex.org/I4210136004","display_name":"University of Bisha","ror":"https://ror.org/040548g92","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210136004"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Hegagi M. Ali","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Bisha, Bisha 61922, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-0159-6726","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Bisha, Bisha 61922, Saudi Arabia","institution_ids":["https://openalex.org/I4210136004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112775980","display_name":"Mahmoud A. Abd-Rabo","orcid":null},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Mahmoud A. Abd-Rabo","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-5063-5301","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt","institution_ids":["https://openalex.org/I184834183"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004188579","display_name":"Haytham M. Rezk","orcid":"https://orcid.org/0000-0001-6782-7908"},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Haytham M. Rezk","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-6782-7908","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt","institution_ids":["https://openalex.org/I184834183"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5004188579"],"corresponding_institution_ids":["https://openalex.org/I184834183"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14820012,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"8","first_page":"624","last_page":"624"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9937000274658203,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9904000163078308,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.7405245304107666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6424320340156555},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.6423856019973755},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5851050615310669},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5736387372016907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3943355679512024},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1911264955997467},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14291471242904663}],"concepts":[{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.7405245304107666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6424320340156555},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.6423856019973755},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5851050615310669},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5736387372016907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3943355679512024},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1911264955997467},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14291471242904663},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14080624","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080624","pdf_url":"https://www.mdpi.com/2075-1680/14/8/624/pdf?version=1755058653","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:641475d896294e778264abd1d429fdf5","is_oa":true,"landing_page_url":"https://doaj.org/article/641475d896294e778264abd1d429fdf5","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":"Axioms, Vol 14, Iss 8, p 624 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14080624","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080624","pdf_url":"https://www.mdpi.com/2075-1680/14/8/624/pdf?version=1755058653","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6933147865","display_name":null,"funder_award_id":"RGP 2/248/46","funder_id":"https://openalex.org/F4320324433","funder_display_name":"King Khalid University"}],"funders":[{"id":"https://openalex.org/F4320319621","display_name":"University of Bisha","ror":"https://ror.org/040548g92"},{"id":"https://openalex.org/F4320324433","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4413127879.pdf","grobid_xml":"https://content.openalex.org/works/W4413127879.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W649798762","https://openalex.org/W1486929028","https://openalex.org/W1534302984","https://openalex.org/W1633315028","https://openalex.org/W1980178787","https://openalex.org/W1982754700","https://openalex.org/W1996820401","https://openalex.org/W2006607804","https://openalex.org/W2015664794","https://openalex.org/W2019007415","https://openalex.org/W2021773803","https://openalex.org/W2022646987","https://openalex.org/W2028337553","https://openalex.org/W2033739016","https://openalex.org/W2035106635","https://openalex.org/W2045776586","https://openalex.org/W2047807008","https://openalex.org/W2061339363","https://openalex.org/W2068981255","https://openalex.org/W2086488349","https://openalex.org/W2197887806","https://openalex.org/W2247216366","https://openalex.org/W2309468965","https://openalex.org/W2340171337","https://openalex.org/W2512209573","https://openalex.org/W2524971255","https://openalex.org/W2525609638","https://openalex.org/W2621244846","https://openalex.org/W2724980447","https://openalex.org/W2984429772","https://openalex.org/W3093997535","https://openalex.org/W4230211289","https://openalex.org/W4309686613","https://openalex.org/W6687686431","https://openalex.org/W6697997958","https://openalex.org/W6704164431","https://openalex.org/W6727714058","https://openalex.org/W6740579433"],"related_works":["https://openalex.org/W2027202866","https://openalex.org/W3149920197","https://openalex.org/W4293569346","https://openalex.org/W2397056152","https://openalex.org/W2494658963","https://openalex.org/W4252904065","https://openalex.org/W3017235236","https://openalex.org/W2949885877","https://openalex.org/W2129544565","https://openalex.org/W2021863153"],"abstract_inverted_index":{"This":[0],"study":[1],"focuses":[2],"on":[3],"analyzing":[4],"the":[5,27,30,35,40,89,96,107],"generalized":[6,97],"HSC-KdV":[7,98],"equations":[8,63],"characterized":[9],"by":[10],"variable":[11,90],"coefficients":[12,91],"and":[13,34,48,80,82,92],"Wick-type":[14],"stochastic":[15,60,93],"(Wt.S)":[16],"elements.":[17],"To":[18],"derive":[19],"white":[20,49],"noise":[21,50],"functional":[22],"(WNF)":[23],"solutions,":[24],"we":[25,53],"employ":[26],"Hermite":[28],"transform,":[29],"homogeneous":[31],"balance":[32],"principle,":[33],"Fe":[36],"(F-expansion)":[37],"technique.":[38],"Leveraging":[39],"inherent":[41],"connection":[42],"between":[43],"hypercomplex":[44],"system":[45],"(HCS)":[46],"theory":[47],"(WN)":[51],"analysis,":[52],"establish":[54],"a":[55,70],"comprehensive":[56],"framework":[57],"for":[58,87],"exploring":[59],"partial":[61],"differential":[62],"(PDEs)":[64],"involving":[65],"non-Gaussian":[66],"parameters":[67],"(N-GP).":[68],"As":[69],"result,":[71],"exact":[72],"solutions":[73],"expressed":[74],"through":[75],"Jacobi":[76],"elliptic":[77],"functions":[78],"(JEFs)":[79],"trigonometric":[81],"hyperbolic":[83],"forms":[84,94],"are":[85],"obtained":[86],"both":[88],"of":[95],"equations.":[99],"An":[100],"illustrative":[101],"example":[102],"is":[103],"included":[104],"to":[105],"validate":[106],"theoretical":[108],"findings.":[109]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-08-15T00:00:00"}