{"id":"https://openalex.org/W7203742649","doi":"https://doi.org/10.3934/math.20261028","title":"On the soliton sensitivity, lump and analytic solutions of the generalized (3+1)-dimensional P-type nonlinear wave equation","display_name":"On the soliton sensitivity, lump and analytic solutions of the generalized (3+1)-dimensional P-type nonlinear wave equation","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7203742649","doi":"https://doi.org/10.3934/math.20261028"},"language":"en","primary_location":{"id":"doi:10.3934/math.20261028","doi":"https://doi.org/10.3934/math.20261028","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.20261028","pdf_url":"http://www.aimspress.com/aimspress-data/math/2026/8/PDF/math-11-08-1028.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://www.aimspress.com/aimspress-data/math/2026/8/PDF/math-11-08-1028.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5141174159","display_name":"Longjun Zhan","orcid":"https://orcid.org/0000-0001-5916-4825","observed_orcids":["https://orcid.org/0000-0001-5916-4825"]},"institutions":[{"id":"https://openalex.org/I146613903","display_name":"Shanghai Lixin University of Accounting and Finance","ror":"https://ror.org/02g81yf77","country_code":"CN","type":"education","lineage":["https://openalex.org/I146613903"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Longjun Zhan","raw_affiliation_strings":["School of Statistics and Mathematics , Shanghai Lixin University of Accounting and Finance , Shanghai 201209 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics , Shanghai Lixin University of Accounting and Finance , Shanghai 201209 , China","institution_ids":["https://openalex.org/I146613903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078121558","display_name":"Adnan Ahmad Mahmud","orcid":"https://orcid.org/0000-0001-7499-1896","observed_orcids":["https://orcid.org/0000-0001-7499-1896"]},"institutions":[{"id":"https://openalex.org/I80538482","display_name":"Harran University","ror":"https://ror.org/057qfs197","country_code":"TR","type":"education","lineage":["https://openalex.org/I80538482"]},{"id":"https://openalex.org/I908820301","display_name":"Tishk International University","ror":"https://ror.org/03pbhyy22","country_code":"IQ","type":"education","lineage":["https://openalex.org/I908820301"]}],"countries":["IQ","TR"],"is_corresponding":false,"raw_author_name":"Adnan Ahmad Mahmud","raw_affiliation_strings":["Harran University , Faculty of Arts and Sciences , Department of Mathematics , S \u00b8anl\u0131urfa 63290 , T\u00fcrkiye","Information Technology Department , Tishk International University , Kurdistan Region , Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harran University , Faculty of Arts and Sciences , Department of Mathematics , S \u00b8anl\u0131urfa 63290 , T\u00fcrkiye","institution_ids":["https://openalex.org/I80538482"]},{"raw_affiliation_string":"Information Technology Department , Tishk International University , Kurdistan Region , Iraq","institution_ids":["https://openalex.org/I908820301"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048266897","display_name":"Hac\u0131 Mehmet Ba\u015fkonu\u015f","orcid":"https://orcid.org/0000-0003-4085-3625","observed_orcids":["https://orcid.org/0000-0003-4085-3625"]},"institutions":[{"id":"https://openalex.org/I146613903","display_name":"Shanghai Lixin University of Accounting and Finance","ror":"https://ror.org/02g81yf77","country_code":"CN","type":"education","lineage":["https://openalex.org/I146613903"]},{"id":"https://openalex.org/I4210127900","display_name":"Azerbaijan University of Architecture and Construction","ror":"https://ror.org/02shm3a27","country_code":"AZ","type":"education","lineage":["https://openalex.org/I4210127900"]},{"id":"https://openalex.org/I80538482","display_name":"Harran University","ror":"https://ror.org/057qfs197","country_code":"TR","type":"education","lineage":["https://openalex.org/I80538482"]},{"id":"https://openalex.org/I908820301","display_name":"Tishk International University","ror":"https://ror.org/03pbhyy22","country_code":"IQ","type":"education","lineage":["https://openalex.org/I908820301"]}],"countries":["AZ","CN","IQ","TR"],"is_corresponding":false,"raw_author_name":"Haci Mehmet Baskonus","raw_affiliation_strings":["Harran University, Faculty of Arts and Sciences, Department of Mathematics, \u015eanl\u0131urfa 63290, T\u00fcrkiye","Harran University, Faculty of Education, Department of Mathematics and Science Education, \u015eanl\u0131urfa 63190, T\u00fcrkiye","Information Technology Department, Tishk International University, Kurdistan Region, Iraq","School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China","Scientific Research Department, Azerbaijan University of Architecture and Construction, Baku AZ1073, Azerbaijan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harran University, Faculty of Arts and Sciences, Department of Mathematics, \u015eanl\u0131urfa 63290, T\u00fcrkiye","institution_ids":["https://openalex.org/I80538482"]},{"raw_affiliation_string":"Harran University, Faculty of Education, Department of Mathematics and Science Education, \u015eanl\u0131urfa 63190, T\u00fcrkiye","institution_ids":["https://openalex.org/I80538482"]},{"raw_affiliation_string":"Information Technology Department, Tishk International University, Kurdistan Region, Iraq","institution_ids":["https://openalex.org/I908820301"]},{"raw_affiliation_string":"School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China","institution_ids":["https://openalex.org/I146613903"]},{"raw_affiliation_string":"Scientific Research Department, Azerbaijan University of Architecture and Construction, Baku AZ1073, Azerbaijan","institution_ids":["https://openalex.org/I4210127900"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1200,"currency":"USD","value_usd":1200},"apc_paid":{"value":1200,"currency":"USD","value_usd":1200},"fwci":1.5429,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78516765,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"11","issue":"8","first_page":"25652","last_page":"25671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994999766349792,"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":0.9994999766349792,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lump-solutions","display_name":"lump solutions","score":0.7390000224113464},{"id":"https://openalex.org/keywords/analytical-solution","display_name":"analytical solution","score":0.6970000267028809},{"id":"https://openalex.org/keywords/traveling-wave-solutions","display_name":"traveling wave solutions","score":0.7099999785423279},{"id":"https://openalex.org/keywords/singular-solitons","display_name":"singular solitons","score":0.9649999737739563},{"id":"https://openalex.org/keywords/bright-and-dark-solitons","display_name":"bright and dark solitons","score":0.8029999732971191},{"id":"https://openalex.org/keywords/bell-shaped-solitons","display_name":"bell-shaped solitons","score":0.8700000047683716},{"id":"https://openalex.org/keywords/dispersion-parameter","display_name":"dispersion parameter","score":0.734000027179718},{"id":"https://openalex.org/keywords/nonlinear-partial-differential-equations","display_name":"nonlinear partial differential equations","score":0.5569999814033508}],"concepts":[{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.8392000198364258},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6868000030517578},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.652400016784668},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.550599992275238},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5411999821662903},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.5296000242233276},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.51419997215271},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.48249998688697815},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.4799000024795532},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.4535999894142151},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.43939998745918274},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.4375999867916107},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4239000082015991},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.39809998869895935},{"id":"https://openalex.org/C106978608","wikidata":"https://www.wikidata.org/wiki/Q1412691","display_name":"Wave packet","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36800000071525574},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.3573000133037567},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.3481000065803528},{"id":"https://openalex.org/C108779253","wikidata":"https://www.wikidata.org/wiki/Q5282591","display_name":"Dispersive partial differential equation","level":3,"score":0.34689998626708984},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.3382999897003174},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.3262999951839447},{"id":"https://openalex.org/C159785203","wikidata":"https://www.wikidata.org/wiki/Q6345653","display_name":"Kadomtsev\u2013Petviashvili equation","level":4,"score":0.31940001249313354},{"id":"https://openalex.org/C2993172089","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Periodic wave","level":3,"score":0.298799991607666},{"id":"https://openalex.org/C44444269","wikidata":"https://www.wikidata.org/wiki/Q2558473","display_name":"sine-Gordon equation","level":4,"score":0.29280000925064087},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.26759999990463257},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.2597000002861023}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/math.20261028","doi":"https://doi.org/10.3934/math.20261028","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.20261028","pdf_url":"http://www.aimspress.com/aimspress-data/math/2026/8/PDF/math-11-08-1028.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/math.20261028","doi":"https://doi.org/10.3934/math.20261028","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.20261028","pdf_url":"http://www.aimspress.com/aimspress-data/math/2026/8/PDF/math-11-08-1028.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203742649.pdf","grobid_xml":"https://content.openalex.org/works/W7203742649.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1633315028","https://openalex.org/W1979722387","https://openalex.org/W2030669316","https://openalex.org/W2047135677","https://openalex.org/W2050639649","https://openalex.org/W2083332431","https://openalex.org/W2083960709","https://openalex.org/W2980144610","https://openalex.org/W4232650420","https://openalex.org/W4308446897","https://openalex.org/W4383620185","https://openalex.org/W4386304547","https://openalex.org/W4387134655","https://openalex.org/W4391062107","https://openalex.org/W4393280375","https://openalex.org/W4394989059","https://openalex.org/W4398182684","https://openalex.org/W4400772392","https://openalex.org/W4402676592","https://openalex.org/W4405889976","https://openalex.org/W4410121678","https://openalex.org/W4414475331","https://openalex.org/W4417306766","https://openalex.org/W7126382156","https://openalex.org/W7127188386","https://openalex.org/W7128480664","https://openalex.org/W7154472837","https://openalex.org/W7154833775","https://openalex.org/W7163197216"],"related_works":["https://openalex.org/W7169782482","https://openalex.org/W7112008990","https://openalex.org/W4410748442","https://openalex.org/W2368829172","https://openalex.org/W4404445915","https://openalex.org/W4407121875","https://openalex.org/W4213321337","https://openalex.org/W7115014797","https://openalex.org/W7154914108","https://openalex.org/W7128786450"],"abstract_inverted_index":{"In":[0],"this":[1,57,157],"manuscript,":[2],"we":[3,22,103,160],"investigated":[4],"a":[5,14,26,40,137],"generalized":[6,48],"(3+1)-dimensional":[7],"P-type":[8],"nonlinear":[9,27],"wave":[10,35],"equation.":[11],"First,":[12],"for":[13,56,156],"more":[15],"detailed":[16],"analysis":[17,139],"of":[18,61,76,100,118,140,143],"the":[19,47,90,98,115,141,144,179],"studied":[20],"model,":[21],"transformed":[23],"it":[24],"into":[25,171],"ordinary":[28],"differential":[29,175],"equation":[30,43,50,176],"by":[31,131],"utilizing":[32],"an":[33],"appropriate":[34],"transformation":[36],"formula.":[37],"We":[38],"utilized":[39],"modified":[41,122],"Riccati":[42,49,123],"method":[44,126],"(also":[45],"called":[46],"method),":[51],"signifying":[52],"its":[53],"first":[54],"application":[55],"model.":[58,158],"The":[59,82,121],"extraction":[60],"traveling":[62],"waves":[63],"and":[64,69,79,89,110,136,177],"singular":[65],"solitons":[66],"used":[67],"exponential":[68],"hyperbolic":[70],"trigonometric":[71],"functions,":[72],"which":[73,150],"exhibited":[74],"features":[75],"darkness,":[77],"brightness,":[78],"mixed":[80],"states.":[81],"bell-shaped":[83],"soliton,":[84],"or":[85],"solitary":[86],"soliton":[87],"solution,":[88],"rational":[91],"lump":[92],"solution":[93],"were":[94,168],"found.":[95],"To":[96],"enhance":[97],"understanding":[99],"our":[101,119],"findings,":[102],"incorporated":[104],"numerical":[105],"simulations":[106],"in":[107],"both":[108],"two-":[109],"three-dimensional":[111],"representations,":[112],"effectively":[113],"illustrating":[114],"physical":[116],"implications":[117],"results.":[120],"sub-equation":[124],"function":[125],"solutions":[127,164],"extended":[128],"prior":[129],"results":[130],"providing":[132],"explicit":[133],"closed-form":[134],"expressions":[135],"systematic":[138],"role":[142],"dispersion":[145],"parameter":[146],"$":[147],"\\alpha_4":[148],"$,":[149],"had":[151],"not":[152],"been":[153],"previously":[154],"quantified":[155],"Additionally,":[159],"confirmed":[161],"that":[162],"all":[163],"are":[165],"valid;":[166],"they":[167],"substituted":[169],"back":[170],"their":[172],"respective":[173],"partial":[174],"satisfied":[178],"required":[180],"conditions.":[181]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-20T00:00:00"}