{"id":"https://openalex.org/W2994319577","doi":"https://doi.org/10.3390/axioms8040134","title":"Exact Solutions for a Class of Wick-Type Stochastic (3+1)-Dimensional Modified Benjamin\u2013Bona\u2013Mahony Equations","display_name":"Exact Solutions for a Class of Wick-Type Stochastic (3+1)-Dimensional Modified Benjamin\u2013Bona\u2013Mahony Equations","publication_year":2019,"publication_date":"2019-12-03","ids":{"openalex":"https://openalex.org/W2994319577","doi":"https://doi.org/10.3390/axioms8040134","mag":"2994319577"},"language":"en","primary_location":{"id":"doi:10.3390/axioms8040134","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8040134","pdf_url":"https://www.mdpi.com/2075-1680/8/4/134/pdf?version=1575593982","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/2075-1680/8/4/134/pdf?version=1575593982","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053042789","display_name":"Praveen Agarwal","orcid":"https://orcid.org/0000-0001-7556-8942"},"institutions":[{"id":"https://openalex.org/I4210154633","display_name":"Inspiration Innovation Synergy University","ror":"https://ror.org/04d3d5q14","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210154633"]},{"id":"https://openalex.org/I4401726791","display_name":"Anand International College of Engineering","ror":"https://ror.org/05sy8fj60","country_code":null,"type":"education","lineage":["https://openalex.org/I4401726791"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Praveen Agarwal","raw_affiliation_strings":["Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India"],"raw_orcid":"https://orcid.org/0000-0001-7556-8942","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India","institution_ids":["https://openalex.org/I4210154633","https://openalex.org/I4401726791"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048312355","display_name":"Abd\u2010Allah Hyder","orcid":"https://orcid.org/0000-0001-9273-9512"},"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":false,"raw_author_name":"Abd-Allah Hyder","raw_affiliation_strings":["Department of Engineering Mathematics and Physics, Faculty of Engineering Al-Azhar University, Cairo P.O. Box 11371, Egypt","Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-9273-9512","affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics and Physics, Faculty of Engineering Al-Azhar University, Cairo P.O. Box 11371, Egypt","institution_ids":["https://openalex.org/I184834183"]},{"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/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":false,"raw_author_name":"M. 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 P.O. Box 71524, Egypt"],"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"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut P.O. Box 71524, Egypt","institution_ids":["https://openalex.org/I184834183"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002110465","display_name":"Ghada AlNemer","orcid":"https://orcid.org/0000-0002-2222-7973"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ghada AlNemer","raw_affiliation_strings":["Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 105862, Riyadh 11656, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-2222-7973","affiliations":[{"raw_affiliation_string":"Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 105862, Riyadh 11656, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080017749","display_name":"Clemente Cesarano","orcid":"https://orcid.org/0000-0002-1694-7907"},"institutions":[{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Clemente Cesarano","raw_affiliation_strings":["Section of Mathematics, Universit\u00e0 Telematica Internazionale Uninettuno, 00186 Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section of Mathematics, Universit\u00e0 Telematica Internazionale Uninettuno, 00186 Rome, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010840230","display_name":"Dario Assante","orcid":"https://orcid.org/0000-0001-9333-5034"},"institutions":[{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Dario Assante","raw_affiliation_strings":["Faculty of Engineering, Universit\u00e0 Telematica Internazionale Uninettuno, 00186 Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9333-5034","affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Universit\u00e0 Telematica Internazionale Uninettuno, 00186 Rome, Italy","institution_ids":["https://openalex.org/I4210155399"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5080017749"],"corresponding_institution_ids":["https://openalex.org/I4210155399"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.5916,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.90555417,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"8","issue":"4","first_page":"134","last_page":"134"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9914000034332275,"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":0.7581535577774048},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.7153247594833374},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.6328513622283936},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.6150363683700562},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.609474241733551},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5691516995429993},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.5582159757614136},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.550062894821167},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5068653225898743},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.43091660737991333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09151485562324524},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05676528811454773}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7581535577774048},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.7153247594833374},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.6328513622283936},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.6150363683700562},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.609474241733551},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5691516995429993},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.5582159757614136},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.550062894821167},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5068653225898743},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43091660737991333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09151485562324524},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05676528811454773},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/axioms8040134","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8040134","pdf_url":"https://www.mdpi.com/2075-1680/8/4/134/pdf?version=1575593982","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:mdpi.com:/2075-1680/8/4/134/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms8040134","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 8; Issue 4; Pages: 134","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms8040134","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8040134","pdf_url":"https://www.mdpi.com/2075-1680/8/4/134/pdf?version=1575593982","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2994319577.pdf","grobid_xml":"https://content.openalex.org/works/W2994319577.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1534302984","https://openalex.org/W1538260139","https://openalex.org/W1659355396","https://openalex.org/W1818445224","https://openalex.org/W1852007522","https://openalex.org/W1973220666","https://openalex.org/W1979722387","https://openalex.org/W1980178787","https://openalex.org/W1987119916","https://openalex.org/W1990902908","https://openalex.org/W1999428409","https://openalex.org/W2005380085","https://openalex.org/W2008423710","https://openalex.org/W2011133013","https://openalex.org/W2030399604","https://openalex.org/W2061496940","https://openalex.org/W2067302693","https://openalex.org/W2072190359","https://openalex.org/W2073817609","https://openalex.org/W2081177783","https://openalex.org/W2119838320","https://openalex.org/W2129310048","https://openalex.org/W2132155190","https://openalex.org/W2140895997","https://openalex.org/W2505733969","https://openalex.org/W2524971255","https://openalex.org/W2621244846","https://openalex.org/W2735661094","https://openalex.org/W2769373305","https://openalex.org/W2917990228","https://openalex.org/W2943623853","https://openalex.org/W2963091121","https://openalex.org/W3011948622","https://openalex.org/W3032535486","https://openalex.org/W4230211289","https://openalex.org/W6632452271","https://openalex.org/W6638727942","https://openalex.org/W6647849778","https://openalex.org/W6651833623","https://openalex.org/W6680982464","https://openalex.org/W6759630599","https://openalex.org/W6775075745","https://openalex.org/W6779059841"],"related_works":["https://openalex.org/W4313655736","https://openalex.org/W3004912959","https://openalex.org/W2087445666","https://openalex.org/W3114797680","https://openalex.org/W2913252231","https://openalex.org/W3176193352","https://openalex.org/W3089008375","https://openalex.org/W2047182136","https://openalex.org/W4386850153","https://openalex.org/W4385498736"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,35,68,86],"investigate":[4],"the":[5,19,24,46,62,75,89],"Wick-type":[6,76],"stochastic":[7,70,77,90],"(3+1)-dimensional":[8,47,78],"modified":[9,20,26,48,79],"Benjamin\u2013Bona\u2013Mahony":[10],"(BBM)":[11],"equations.":[12,50,81],"We":[13],"present":[14],"a":[15,37],"generalised":[16],"version":[17],"of":[18,40,55,64],"tanh\u2013coth":[21,27],"method.":[22],"Using":[23],"generalised,":[25],"method,":[28],"white":[29,96],"noise":[30,97],"theory,":[31],"and":[32,58],"Hermite":[33,66],"transform,":[34,67],"produce":[36],"new":[38],"set":[39,52],"exact":[41],"travelling":[42,71],"wave":[43,72],"solutions":[44,54,73,91],"for":[45,74],"BBM":[49,80],"This":[51],"includes":[53],"exponential,":[56],"hyperbolic,":[57],"trigonometric":[59],"types.":[60],"With":[61],"help":[63],"inverse":[65],"obtained":[69],"Eventually,":[82],"by":[83],"application":[84],"example,":[85],"show":[87],"how":[88],"can":[92],"be":[93],"given":[94],"as":[95],"functional":[98],"solutions.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":13}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2019-12-13T00:00:00"}
