{"id":"https://openalex.org/W4404668448","doi":"https://doi.org/10.3390/sym16121572","title":"Travelling Solitary Wave Solutions to Non-Gaussian \u03c7-Wick-Type Stochastic Burgers\u2019 Equation with Variable Coefficients","display_name":"Travelling Solitary Wave Solutions to Non-Gaussian \u03c7-Wick-Type Stochastic Burgers\u2019 Equation with Variable Coefficients","publication_year":2024,"publication_date":"2024-11-24","ids":{"openalex":"https://openalex.org/W4404668448","doi":"https://doi.org/10.3390/sym16121572"},"language":"en","primary_location":{"id":"doi:10.3390/sym16121572","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16121572","pdf_url":null,"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://doi.org/10.3390/sym16121572","any_repository_has_fulltext":false},"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/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]},{"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":["EG","SA"],"is_corresponding":true,"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","Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt"],"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"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt","institution_ids":["https://openalex.org/I184834183"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109786638","display_name":"M. M. Alqarni","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":"Manal Al-Qarni","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":"last","author":{"id":"https://openalex.org/A5031028854","display_name":"Tahani Al-Qahtani","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":"Tahani Al-Qahtani","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"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060547119"],"corresponding_institution_ids":["https://openalex.org/I184834183","https://openalex.org/I82952536"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19284808,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"12","first_page":"1572","last_page":"1572"},"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/T10988","display_name":"Advanced Fiber Laser Technologies","score":0.9904000163078308,"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":0.9890000224113464,"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/mathematics","display_name":"Mathematics","score":0.7319080829620361},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.659582257270813},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6041254997253418},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.5991331338882446},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5300880074501038},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.518043041229248},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.5069230198860168},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4707240164279938},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.46418967843055725},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4375007748603821},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.434359610080719},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.42542946338653564},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.41302186250686646},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23777121305465698}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7319080829620361},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.659582257270813},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6041254997253418},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.5991331338882446},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5300880074501038},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.518043041229248},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.5069230198860168},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4707240164279938},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.46418967843055725},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4375007748603821},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.434359610080719},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.42542946338653564},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.41302186250686646},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23777121305465698},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16121572","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16121572","pdf_url":null,"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:a9664771102d4e83aa287abc92bee02e","is_oa":false,"landing_page_url":"https://doaj.org/article/a9664771102d4e83aa287abc92bee02e","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 12, p 1572 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16121572","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16121572","pdf_url":null,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1534302984","https://openalex.org/W1538260139","https://openalex.org/W1981512412","https://openalex.org/W1999428409","https://openalex.org/W2005380085","https://openalex.org/W2119838320","https://openalex.org/W2129310048","https://openalex.org/W2309468965","https://openalex.org/W2512209573","https://openalex.org/W2524971255","https://openalex.org/W2525609638","https://openalex.org/W2621244846","https://openalex.org/W2941387609","https://openalex.org/W3093325265","https://openalex.org/W3103352361","https://openalex.org/W4230211289","https://openalex.org/W4308207202","https://openalex.org/W6632452271","https://openalex.org/W6651833623","https://openalex.org/W6697997958","https://openalex.org/W6727714058","https://openalex.org/W6761802674"],"related_works":["https://openalex.org/W2298119490","https://openalex.org/W2901682677","https://openalex.org/W196401064","https://openalex.org/W2016693765","https://openalex.org/W2069080898","https://openalex.org/W2130974430","https://openalex.org/W2237950066","https://openalex.org/W1985306637","https://openalex.org/W4365137133","https://openalex.org/W3202710143"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3],"obtain":[4],"non-Gaussian":[5,48],"(NG)":[6],"stochastic":[7,11],"solutions":[8,51,63],"to":[9,53,65],"\u03c7-Wick-type":[10],"(\u03c7-Wk-TS)":[12],"Burgers\u2019":[13,54,67],"equations":[14,55,68,80],"with":[15,56,69],"variable":[16,57,70],"coefficients.":[17,58],"An":[18],"Exp-function":[19],"method,":[20],"the":[21,31,82,91],"connection":[22],"between":[23],"white":[24,60],"noise":[25,61],"theory":[26],"and":[27,35,81],"hypercomplex":[28],"systems":[29],"(HCSs),":[30],"\u03c7-Wick":[32],"product":[33],"(\u03c7-Wk-product)":[34],"an":[36],"\u03c7-Hermite":[37],"transform":[38],"(\u03c7-Hr-transform)":[39],"are":[40,72,87],"proposed.":[41],"We":[42],"provide":[43],"a":[44],"new":[45],"set":[46],"of":[47,77,85],"solitary":[49],"wave":[50],"(NG-SWSs)":[52],"NG":[59],"functional":[62],"(NG-WNFSs)":[64],"\u03c7-Wk-TS":[66],"coefficients":[71,76],"shown.":[73],"The":[74],"symmetry":[75],"partial":[78],"differential":[79],"symmetrical":[83],"properties":[84],"SPDEs":[86],"critical":[88],"in":[89],"determining":[90],"best":[92],"solution.":[93]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}