{"id":"https://openalex.org/W2146167112","doi":null,"title":"New Exact Traveling Wave Solutions for the Nonlinear Klein-Gordon Equation","display_name":"New Exact Traveling Wave Solutions for the Nonlinear Klein-Gordon Equation","publication_year":2008,"publication_date":"2008-08-25","ids":{"openalex":"https://openalex.org/W2146167112","mag":"2146167112"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.930.3344","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.930.3344","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://journals.tubitak.gov.tr/physics/issues/fiz-08-32-5/fiz-32-5-1-0804-1.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079361890","display_name":"Zaiyun Zhang","orcid":"https://orcid.org/0000-0002-5365-2753","observed_orcids":["https://orcid.org/0000-0002-5365-2753"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zaiyun Zhang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5365-2753","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5079361890"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3582,"has_fulltext":false,"cited_by_count":70,"citation_normalized_percentile":{"value":0.79943115,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":100},"biblio":{"volume":"32","issue":"5","first_page":"235","last_page":"240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9990000128746033,"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":0.9990000128746033,"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":0.00019999999494757503,"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":9.999999747378752e-05,"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-klein-gordon-equation","display_name":"nonlinear Klein-Gordon equation","score":0.9990000128746033},{"id":"https://openalex.org/keywords/traveling-wave-solutions","display_name":"traveling wave solutions","score":0.9959999918937683},{"id":"https://openalex.org/keywords/exact-solutions","display_name":"exact solutions","score":0.8040000200271606}],"concepts":[{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.8087524175643921},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.7224401831626892},{"id":"https://openalex.org/C2993172089","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Periodic wave","level":3,"score":0.7156879901885986},{"id":"https://openalex.org/C101682238","wikidata":"https://www.wikidata.org/wiki/Q868967","display_name":"Klein\u2013Gordon equation","level":3,"score":0.6822417974472046},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.6563031673431396},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5964783430099487},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5360358953475952},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5088701248168945},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4764578640460968},{"id":"https://openalex.org/C106978608","wikidata":"https://www.wikidata.org/wiki/Q1412691","display_name":"Wave packet","level":2,"score":0.4692176580429077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.450540691614151},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.34156447649002075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29526665806770325},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12469726800918579},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07144096493721008},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.930.3344","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.930.3344","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://journals.tubitak.gov.tr/physics/issues/fiz-08-32-5/fiz-32-5-1-0804-1.pdf","raw_type":"text"},{"id":"pmh:oai:dergipark.gov.tr:article/149277","doi":null,"is_oa":false,"landing_page_url":"http://dergipark.gov.tr/tbtkphysics/issue/12413/149277","pdf_url":null,"source":{"id":"https://openalex.org/S4306401840","display_name":"DergiPark (Istanbul University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67581229","host_organization_name":"Istanbul University","host_organization_lineage":["https://openalex.org/I67581229"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"\\n Volume: 32, Issue: 5\\n 235-240\\n \\n","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dergipark.org.tr:article/149277","doi":null,"is_oa":false,"landing_page_url":"https://dergipark.org.tr/tr/pub/tbtkphysics/issue/12413/149277","pdf_url":null,"source":{"id":"https://openalex.org/S4306401840","display_name":"DergiPark (Istanbul University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67581229","host_organization_name":"Istanbul University","host_organization_lineage":["https://openalex.org/I67581229"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"\\n Volume: 32, Issue: 5\\n 235-240\\n \\n","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:2146167112","doi":null,"is_oa":false,"landing_page_url":"http://journals.tubitak.gov.tr/physics/issues/fiz-08-32-5/fiz-32-5-1-0804-1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2765045320","display_name":"TURKISH JOURNAL OF PHYSICS","issn_l":"1300-0101","issn":["1300-0101","1303-6122"],"is_oa":false,"is_in_doaj":true,"is_core":false,"listed_in":["ddh","doaj","dongbi-c","norway-1","poland-20","russia-white-list-3","tr-dizin"],"host_organization":"https://openalex.org/P4310318422","host_organization_name":"Scientific and Technological Research Council of Turkey (TUBITAK)","host_organization_lineage":["https://openalex.org/P4310318422"],"host_organization_lineage_names":["Scientific and Technological Research Council of Turkey (TUBITAK)"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"TURKISH JOURNAL OF PHYSICS","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2037065062","https://openalex.org/W2083960709"],"related_works":["https://openalex.org/W7099988798","https://openalex.org/W1966835893","https://openalex.org/W2331755966","https://openalex.org/W2046624340","https://openalex.org/W2359941688","https://openalex.org/W2348815742","https://openalex.org/W2188883854","https://openalex.org/W2080016959","https://openalex.org/W1969535193","https://openalex.org/W2358467931"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,10],"discuss":[4],"the":[5,12],"nonlinear":[6],"Klein-Gordon":[7],"equation":[8],"and":[9,34],"derive":[11],"new":[13],"traveling":[14],"wave":[15,32,37],"solutions":[16,33],"by":[17],"applying":[18],"trigonometric":[19],"function":[20],"series":[21],"method.":[22],"Also,":[23],"they":[24],"are":[25],"complex":[26],"linear":[27],"combinations":[28],"of":[29],"kink":[30],"solitary":[31,36],"bell":[35],"solutions.":[38]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}