{"id":"https://openalex.org/W4380990186","doi":"https://doi.org/10.3390/axioms12060599","title":"The Investigation of Dynamical Behavior of Benjamin\u2013Bona\u2013Mahony\u2013Burger Equation with Different Differential Operators Using Two Analytical Approaches","display_name":"The Investigation of Dynamical Behavior of Benjamin\u2013Bona\u2013Mahony\u2013Burger Equation with Different Differential Operators Using Two Analytical Approaches","publication_year":2023,"publication_date":"2023-06-16","ids":{"openalex":"https://openalex.org/W4380990186","doi":"https://doi.org/10.3390/axioms12060599"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12060599","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12060599","pdf_url":"https://www.mdpi.com/2075-1680/12/6/599/pdf?version=1686924203","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/2075-1680/12/6/599/pdf?version=1686924203","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100701457","display_name":"Xiaoming Wang","orcid":"https://orcid.org/0000-0002-5581-8796"},"institutions":[{"id":"https://openalex.org/I10496686","display_name":"Shangrao Normal University","ror":"https://ror.org/024qkwh22","country_code":"CN","type":"education","lineage":["https://openalex.org/I10496686"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoming Wang","raw_affiliation_strings":["School of Mathematics & Computer Science, Shangrao Normal University, Shangrao 334001, China"],"raw_orcid":"https://orcid.org/0000-0002-5581-8796","affiliations":[{"raw_affiliation_string":"School of Mathematics & Computer Science, Shangrao Normal University, Shangrao 334001, China","institution_ids":["https://openalex.org/I10496686"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092188805","display_name":"Rimsha Ansar","orcid":null},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Rimsha Ansar","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036734666","display_name":"Muhammad Abbas","orcid":"https://orcid.org/0000-0002-0491-1528"},"institutions":[{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Abbas","raw_affiliation_strings":["Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-0491-1528","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019785333","display_name":"Farah Aini Abdullah","orcid":"https://orcid.org/0000-0002-5215-9617"},"institutions":[{"id":"https://openalex.org/I139322472","display_name":"Universiti Sains Malaysia","ror":"https://ror.org/02rgb2k63","country_code":"MY","type":"education","lineage":["https://openalex.org/I139322472"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Farah Aini Abdullah","raw_affiliation_strings":["School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-5215-9617","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia","institution_ids":["https://openalex.org/I139322472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077715487","display_name":"Khadijah M. Abualnaja","orcid":"https://orcid.org/0000-0002-2908-1807"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Khadijah M. Abualnaja","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-2908-1807","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5036734666"],"corresponding_institution_ids":["https://openalex.org/I160968435"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.0911,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.75090182,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"12","issue":"6","first_page":"599","last_page":"599"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9991000294685364,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9815999865531921,"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/mathematical-analysis","display_name":"Mathematical analysis","score":0.5768353343009949},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5562757849693298},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5254278182983398},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.496479332447052},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48931214213371277},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.4885757863521576},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.4859253466129303},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4826505780220032},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4665256440639496},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39937302470207214},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.37153360247612},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.33331161737442017},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3141273856163025},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1160622239112854}],"concepts":[{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5768353343009949},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5562757849693298},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5254278182983398},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.496479332447052},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48931214213371277},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.4885757863521576},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.4859253466129303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4826505780220032},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4665256440639496},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39937302470207214},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.37153360247612},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.33331161737442017},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3141273856163025},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1160622239112854},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms12060599","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12060599","pdf_url":"https://www.mdpi.com/2075-1680/12/6/599/pdf?version=1686924203","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:0d44a6c57f6d46ce98e539de59c60e37","is_oa":true,"landing_page_url":"https://doaj.org/article/0d44a6c57f6d46ce98e539de59c60e37","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 12, Iss 6, p 599 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms12060599","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12060599","pdf_url":"https://www.mdpi.com/2075-1680/12/6/599/pdf?version=1686924203","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/G3883638043","display_name":"\u9971\u548c\u975e\u7ebf\u6027\u859b\u5b9a\u8c14\u65b9\u7a0b\u7684\u53d8\u5206\u65b9\u6cd5\u4e0e\u5b9a\u6027\u7814\u7a76","funder_award_id":"11861053","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323722","display_name":"Taif University","ror":"https://ror.org/014g1a453"},{"id":"https://openalex.org/F4320325626","display_name":"Education Department of Jiangxi Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4380990186.pdf"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W566301135","https://openalex.org/W1966553738","https://openalex.org/W1989760690","https://openalex.org/W2003404223","https://openalex.org/W2018661297","https://openalex.org/W2053757777","https://openalex.org/W2056657364","https://openalex.org/W2061233345","https://openalex.org/W2063067239","https://openalex.org/W2079666300","https://openalex.org/W2117693140","https://openalex.org/W2510717660","https://openalex.org/W2556784265","https://openalex.org/W2567181934","https://openalex.org/W2602496407","https://openalex.org/W2908577864","https://openalex.org/W2924176122","https://openalex.org/W2934421207","https://openalex.org/W2963520255","https://openalex.org/W2963641381","https://openalex.org/W3024925239","https://openalex.org/W3035234532","https://openalex.org/W3095298597","https://openalex.org/W3120095522","https://openalex.org/W3151368905","https://openalex.org/W3213503458","https://openalex.org/W4213321337","https://openalex.org/W4286782156","https://openalex.org/W4296360172","https://openalex.org/W4313361151","https://openalex.org/W4316805817","https://openalex.org/W4323846871","https://openalex.org/W4361306868","https://openalex.org/W4362473463","https://openalex.org/W4367598976","https://openalex.org/W4381322605","https://openalex.org/W6730176618","https://openalex.org/W6844433889"],"related_works":["https://openalex.org/W3134495997","https://openalex.org/W2371448224","https://openalex.org/W2363680170","https://openalex.org/W2376428685","https://openalex.org/W625783435","https://openalex.org/W2048742619","https://openalex.org/W2384641672","https://openalex.org/W2277501881","https://openalex.org/W2366004374","https://openalex.org/W2391580480"],"abstract_inverted_index":{"The":[0,15,69,114,132],"dynamic":[1,67],"behavior":[2,143],"variation":[3],"of":[4,27,48,54,108,123,144],"the":[5,28,42,49,55,78,82,104,109,121,142],"Benjamin\u2013Bona\u2013Mahony\u2013Burger":[6],"(BBM-Burger)":[7],"equation":[8,18,116],"has":[9],"been":[10,138],"investigated":[11],"in":[12,119,127],"this":[13],"paper.":[14],"modified":[16],"auxiliary":[17],"method":[19],"(MAEM)":[20],"and":[21,31,60,71,95,134],"Ricatti\u2013Bernoulli":[22],"(RB)":[23],"sub-ODE":[24],"method,":[25],"two":[26],"most":[29],"reliable":[30],"useful":[32],"analytical":[33,79,145],"approaches,":[34],"are":[35,74,100],"used":[36,75],"to":[37,64,76,140],"construct":[38],"soliton":[39,98],"solutions":[40,51,80,99],"for":[41,81],"proposed":[43],"model.":[44,84],"We":[45,102],"demonstrate":[46],"some":[47],"extracted":[50],"using":[52],"definitions":[53],"\u03b2-derivative,":[56],"conformable":[57],"derivative":[58],"(CD),":[59],"M-truncated":[61],"derivatives":[62,110],"(M-TD)":[63],"understand":[65],"their":[66],"behavior.":[68],"hyperbolic":[70],"trigonometric":[72],"functions":[73],"derive":[77],"given":[83],"As":[85],"a":[86],"consequence,":[87],"dark,":[88],"bell-shaped,":[89],"anti-bell,":[90],"M-shaped,":[91],"W-shaped,":[92],"kink":[93],"soliton,":[94],"solitary":[96],"wave":[97,146],"obtained.":[101],"observe":[103],"fractional":[105],"parameter":[106],"impact":[107],"on":[111],"physical":[112],"phenomena.":[113],"BBM-Burger":[115],"is":[117],"functional":[118],"describing":[120],"propagation":[122],"long":[124],"unidirectional":[125],"waves":[126],"many":[128],"nonlinear":[129],"diffusive":[130],"systems.":[131],"2D":[133],"3D":[135],"graphs":[136],"have":[137],"presented":[139],"confirm":[141],"solutions.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2023-06-17T00:00:00"}
