{"id":"https://openalex.org/W2586608768","doi":"https://doi.org/10.3390/e19020060","title":"Nonlinear Wave Equations Related to Nonextensive Thermostatistics","display_name":"Nonlinear Wave Equations Related to Nonextensive Thermostatistics","publication_year":2017,"publication_date":"2017-02-07","ids":{"openalex":"https://openalex.org/W2586608768","doi":"https://doi.org/10.3390/e19020060","mag":"2586608768"},"language":"en","primary_location":{"id":"doi:10.3390/e19020060","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19020060","pdf_url":"https://www.mdpi.com/1099-4300/19/2/60/pdf?version=1486466323","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/19/2/60/pdf?version=1486466323","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059654447","display_name":"A. Plastino","orcid":"https://orcid.org/0000-0001-5848-0770"},"institutions":[{"id":"https://openalex.org/I3130568980","display_name":"National University of Northwestern Buenos Aires","ror":"https://ror.org/00c8e6e47","country_code":"AR","type":"education","lineage":["https://openalex.org/I3130568980"]}],"countries":["AR"],"is_corresponding":true,"raw_author_name":"Angel Plastino","raw_affiliation_strings":["CeBio y Secretar\u00eda de Investigaci\u00f3n, Universidad Nacional del Noroeste de la Prov\u00edncia de Buenos Aires, UNNOBA-Conicet, Roque Saenz Pe\u00f1a 456, 6000 Junin, Argentina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CeBio y Secretar\u00eda de Investigaci\u00f3n, Universidad Nacional del Noroeste de la Prov\u00edncia de Buenos Aires, UNNOBA-Conicet, Roque Saenz Pe\u00f1a 456, 6000 Junin, Argentina","institution_ids":["https://openalex.org/I3130568980"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076828245","display_name":"Roseli S. Wedemann","orcid":"https://orcid.org/0000-0001-7532-3881"},"institutions":[{"id":"https://openalex.org/I40034438","display_name":"Universidade do Estado do Rio de Janeiro","ror":"https://ror.org/0198v2949","country_code":"BR","type":"education","lineage":["https://openalex.org/I40034438"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Roseli Wedemann","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade do Estado do Rio de Janeiro, Rua S\u00e3o Francisco Xavier, 524, 20550-900 Rio de Janeiro, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-7532-3881","affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade do Estado do Rio de Janeiro, Rua S\u00e3o Francisco Xavier, 524, 20550-900 Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I40034438"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059654447"],"corresponding_institution_ids":["https://openalex.org/I3130568980"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.499,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.81087158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"2","first_page":"60","last_page":"60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9997000098228455,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9997000098228455,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.940500020980835,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9391999840736389,"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/nonlinear-system","display_name":"Nonlinear system","score":0.7020074129104614},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.5731934309005737},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5619252920150757},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.5395895838737488},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5260791182518005},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5233998894691467},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5222359895706177},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.48305779695510864},{"id":"https://openalex.org/keywords/plane-wave","display_name":"Plane wave","score":0.4826658070087433},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.46397432684898376},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3946875333786011},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34108293056488037},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33205336332321167},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.28480613231658936}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7020074129104614},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.5731934309005737},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5619252920150757},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.5395895838737488},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5260791182518005},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5233998894691467},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5222359895706177},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.48305779695510864},{"id":"https://openalex.org/C40308292","wikidata":"https://www.wikidata.org/wiki/Q122518","display_name":"Plane wave","level":2,"score":0.4826658070087433},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.46397432684898376},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3946875333786011},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34108293056488037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33205336332321167},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.28480613231658936},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e19020060","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19020060","pdf_url":"https://www.mdpi.com/1099-4300/19/2/60/pdf?version=1486466323","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:ri.conicet.gov.ar:11336/72828","is_oa":true,"landing_page_url":"http://hdl.handle.net/11336/72828","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"reponame:CONICET Digital (CONICET)","raw_type":"http://purl.org/coar/resource_type/c_6501"},{"id":"pmh:oai:doaj.org/article:da07498e14c842a1b314fbc57c4ee96d","is_oa":true,"landing_page_url":"https://doaj.org/article/da07498e14c842a1b314fbc57c4ee96d","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":"Entropy, Vol 19, Iss 2, p 60 (2017)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/19/2/60/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e19020060","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":"Entropy; Volume 19; Issue 2; Pages: 60","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e19020060","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19020060","pdf_url":"https://www.mdpi.com/1099-4300/19/2/60/pdf?version=1486466323","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4000000059604645}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322749","display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","ror":"https://ror.org/03kk0s825"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2586608768.pdf","grobid_xml":"https://content.openalex.org/works/W2586608768.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1527617228","https://openalex.org/W1600090841","https://openalex.org/W1625147614","https://openalex.org/W1752533918","https://openalex.org/W1873431535","https://openalex.org/W1967496927","https://openalex.org/W1983874169","https://openalex.org/W1988682493","https://openalex.org/W1996438272","https://openalex.org/W2017963899","https://openalex.org/W2019417347","https://openalex.org/W2027615116","https://openalex.org/W2040183387","https://openalex.org/W2044756742","https://openalex.org/W2051014254","https://openalex.org/W2067559246","https://openalex.org/W2076860865","https://openalex.org/W2078477559","https://openalex.org/W2079413089","https://openalex.org/W2082189977","https://openalex.org/W2094385303","https://openalex.org/W2135779339","https://openalex.org/W2148772257","https://openalex.org/W2152008523","https://openalex.org/W2161811246","https://openalex.org/W2170439816","https://openalex.org/W2208655342","https://openalex.org/W2240510098","https://openalex.org/W2273394904","https://openalex.org/W2302503768","https://openalex.org/W2314520473","https://openalex.org/W2327289687","https://openalex.org/W2413325692","https://openalex.org/W2514692830","https://openalex.org/W2531289303","https://openalex.org/W3098913786","https://openalex.org/W3100556136","https://openalex.org/W3102435600","https://openalex.org/W3102616287","https://openalex.org/W3104492505"],"related_works":["https://openalex.org/W2245214771","https://openalex.org/W2073973926","https://openalex.org/W2333053900","https://openalex.org/W1975562467","https://openalex.org/W2951961089","https://openalex.org/W3101208931","https://openalex.org/W2181923191","https://openalex.org/W3213209941","https://openalex.org/W4293767864","https://openalex.org/W2074095400"],"abstract_inverted_index":{"We":[0],"advance":[1],"two":[2],"nonlinear":[3,30,70,138,150,159,169],"wave":[4,46,59,71,87,118,139,145],"equations":[5,51,72,119,140],"related":[6],"to":[7,132],"the":[8,14,34,41,53,69,81,103,112,137],"nonextensive":[9,115],"thermostatistical":[10],"formalism":[11,36],"based":[12],"upon":[13],"power-law":[15],"nonadditive":[16],"S":[17],"q":[18],"entropies.":[19],"Our":[20],"present":[21],"contribution":[22],"is":[23,143,167],"in":[24,123],"line":[25],"with":[26,63,148],"recent":[27,65],"developments,":[28,66],"where":[29],"extensions":[31],"inspired":[32],"on":[33],"q-thermostatistical":[35],"have":[37],"been":[38],"proposed":[39],"for":[40],"Schroedinger,":[42],"Klein\u2013Gordon,":[43],"and":[44,80,105,153],"Dirac":[45],"equations.":[47],"These":[48,93],"previously":[49],"introduced":[50],"share":[52],"interesting":[54],"feature":[55],"of":[56,68,102,114,136],"admitting":[57],"q-plane":[58],"solutions.":[60],"In":[61],"contrast":[62],"these":[64],"one":[67,83],"that":[73,120],"we":[74,121,165],"propose":[75],"exhibits":[76],"real":[77],"q-Gaussian":[78],"solutions,":[79],"other":[82,163],"admits":[84],"exponential":[85],"plane":[86],"solutions":[88],"modulated":[89],"by":[90],"a":[91,144,149,158,168],"q-Gaussian.":[92],"q-Gaussians":[94,109],"are":[95,99,110],"q-exponentials":[96],"whose":[97],"arguments":[98],"quadratic":[100],"functions":[101],"space":[104],"time":[106],"variables.":[107],"The":[108,117,162],"at":[111],"heart":[113],"thermostatistics.":[116],"analyze":[122],"this":[124],"work":[125],"illustrate":[126],"new":[127],"possible":[128],"dynamical":[129],"scenarios":[130],"leading":[131],"time-dependent":[133],"q-Gaussians.":[134],"One":[135],"considered":[141],"here":[142],"equation":[146,164],"endowed":[147],"potential":[151],"term,":[152],"can":[154],"be":[155],"regarded":[156],"as":[157],"Klein\u2013Gordon":[160],"equation.":[161,171],"study":[166],"Schroedinger-like":[170]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2017-02-17T00:00:00"}
