{"id":"https://openalex.org/W4411451733","doi":"https://doi.org/10.3390/axioms14060477","title":"Abundant Exact Traveling-Wave Solutions for Stochastic Graphene Sheets Model","display_name":"Abundant Exact Traveling-Wave Solutions for Stochastic Graphene Sheets Model","publication_year":2025,"publication_date":"2025-06-19","ids":{"openalex":"https://openalex.org/W4411451733","doi":"https://doi.org/10.3390/axioms14060477"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14060477","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060477","pdf_url":"https://www.mdpi.com/2075-1680/14/6/477/pdf?version=1750340731","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/2075-1680/14/6/477/pdf?version=1750340731","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061698030","display_name":"Wael W. Mohammed","orcid":"https://orcid.org/0000-0002-1402-7584"},"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":true,"raw_author_name":"Wael W. Mohammed","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia","Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-1402-7584","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021878148","display_name":"Taher S. Hassan","orcid":"https://orcid.org/0000-0003-2907-3353"},"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":"Taher S. Hassan","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia","Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-2907-3353","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014091363","display_name":"Rabeb Sidaoui","orcid":"https://orcid.org/0000-0001-5965-6619"},"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":"Rabeb Sidaoui","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia","Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106608675","display_name":"Hijyah M. Alshammary","orcid":null},"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":"Hijyah Alshammary","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia","Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071528345","display_name":"Mohamed S. Algolam","orcid":"https://orcid.org/0000-0003-4005-9595"},"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":"Mohamed S. Algolam","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia","Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-4005-9595","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5061698030"],"corresponding_institution_ids":["https://openalex.org/I4210088963"],"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":0.10234451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"6","first_page":"477","last_page":"477"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9984999895095825,"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":0.9984999895095825,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9919999837875366,"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/graphene","display_name":"Graphene","score":0.8902815580368042},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5349321365356445},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.4866521954536438},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4594382643699646},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.43888476490974426},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.42644941806793213},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.42538586258888245},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.41429635882377625},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.40917283296585083},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3684307932853699},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3331412672996521},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2841046452522278},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26567912101745605},{"id":"https://openalex.org/keywords/nanotechnology","display_name":"Nanotechnology","score":0.24069735407829285},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24028003215789795},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1863812506198883},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.17722398042678833},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12840715050697327},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12721973657608032}],"concepts":[{"id":"https://openalex.org/C30080830","wikidata":"https://www.wikidata.org/wiki/Q169917","display_name":"Graphene","level":2,"score":0.8902815580368042},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5349321365356445},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.4866521954536438},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4594382643699646},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.43888476490974426},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.42644941806793213},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.42538586258888245},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.41429635882377625},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.40917283296585083},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3684307932853699},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3331412672996521},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2841046452522278},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26567912101745605},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.24069735407829285},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24028003215789795},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1863812506198883},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.17722398042678833},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12840715050697327},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12721973657608032},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14060477","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060477","pdf_url":"https://www.mdpi.com/2075-1680/14/6/477/pdf?version=1750340731","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:c767660a54aa49cf8581fc8698f815ce","is_oa":true,"landing_page_url":"https://doaj.org/article/c767660a54aa49cf8581fc8698f815ce","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 6, p 477 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14060477","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060477","pdf_url":"https://www.mdpi.com/2075-1680/14/6/477/pdf?version=1750340731","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":[{"display_name":"Affordable and clean energy","score":0.8500000238418579,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411451733.pdf","grobid_xml":"https://content.openalex.org/works/W4411451733.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1983393596","https://openalex.org/W2018661297","https://openalex.org/W2027588087","https://openalex.org/W2053833421","https://openalex.org/W2066336292","https://openalex.org/W2073817609","https://openalex.org/W2084797093","https://openalex.org/W2141112962","https://openalex.org/W2145137020","https://openalex.org/W2781847584","https://openalex.org/W2954110777","https://openalex.org/W4205943247","https://openalex.org/W4231021340","https://openalex.org/W4301484187","https://openalex.org/W4313361151","https://openalex.org/W4367306027","https://openalex.org/W4368370584","https://openalex.org/W4380882256","https://openalex.org/W4399382447","https://openalex.org/W4407052489","https://openalex.org/W6666805008"],"related_works":["https://openalex.org/W4318195686","https://openalex.org/W4251867247","https://openalex.org/W2975999359","https://openalex.org/W3041852390","https://openalex.org/W3119693376","https://openalex.org/W2796561647","https://openalex.org/W4280497496","https://openalex.org/W4313513739","https://openalex.org/W3182422617","https://openalex.org/W2399970821"],"abstract_inverted_index":{"Here,":[0],"we":[1,58,107],"consider":[2],"the":[3,14,20,24,35,41,53,60,64,68,87,90,104,114,120,124,131,135,149,152],"stochastic":[4,47,91,128],"graphene":[5,36,69,73,92,138],"sheets":[6,37,70,74,93],"model":[7,38,94],"(SGSM)":[8],"forced":[9],"by":[10,29],"multiplicative":[11,117],"noise":[12,118],"in":[13,77],"It\u00f4":[15],"sense.":[16],"We":[17],"show":[18],"that":[19,112,133],"exact":[21,121],"solution":[22,45],"of":[23,34,46,67,89,116,123,137,151],"SGSM":[25],"may":[26],"be":[27],"obtained":[28],"solving":[30],"some":[31],"deterministic":[32,65],"counterparts":[33,66],"and":[39,84],"combining":[40],"result":[42],"with":[43],"a":[44],"ordinary":[48],"differential":[49],"equations.":[50],"By":[51,126],"applying":[52],"extended":[54],"tanh":[55],"function":[56],"method,":[57],"obtain":[59],"soliton":[61],"solutions":[62,88,122],"for":[63,97],"model.":[71],"Because":[72],"are":[75,95],"important":[76],"many":[78],"fields,":[79],"such":[80],"as":[81],"electronics,":[82],"photonics,":[83],"energy":[85],"storage,":[86],"beneficial":[96],"understanding":[98],"several":[99,109],"fascinating":[100],"scientific":[101],"phenomena.":[102],"Using":[103],"MATLAB":[105],"program,":[106],"exhibit":[108],"3D":[110],"graphs":[111],"illustrate":[113],"impact":[115,148],"on":[119],"SGSM.":[125],"incorporating":[127],"elements":[129],"into":[130,144],"equations":[132],"govern":[134],"evolution":[136],"sheets,":[139],"researchers":[140],"can":[141],"gain":[142],"insights":[143],"how":[145],"these":[146],"fluctuations":[147],"behavior":[150],"material":[153],"over":[154],"time.":[155]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
