{"id":"https://openalex.org/W7220838602","doi":"https://doi.org/10.1038/s41598-026-74137-8","title":"Uniqueness and structure-preserving numerical simulations for an Ultrahyperbolic Schr\u00f6dinger equation","display_name":"Uniqueness and structure-preserving numerical simulations for an Ultrahyperbolic Schr\u00f6dinger equation","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220838602","doi":"https://doi.org/10.1038/s41598-026-74137-8"},"language":"en","primary_location":{"id":"doi:10.1038/s41598-026-74137-8","doi":"https://doi.org/10.1038/s41598-026-74137-8","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-74137-8","pdf_url":"https://www.nature.com/articles/s41598-026-74137-8_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.nature.com/articles/s41598-026-74137-8_reference.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057792710","display_name":"\u00d6zlem Kaytmaz","orcid":"https://orcid.org/0000-0003-0420-007X","observed_orcids":["https://orcid.org/0000-0003-0420-007X"]},"institutions":[{"id":"https://openalex.org/I3017902709","display_name":"Zonguldak B\u00fclent Ecevit University","ror":"https://ror.org/01dvabv26","country_code":"TR","type":"education","lineage":["https://openalex.org/I3017902709"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"\u00d6zlem Kaytmaz","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Zonguldak B\u00fclent Ecevit University, Zonguldak, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Zonguldak B\u00fclent Ecevit University, Zonguldak, Turkey","institution_ids":["https://openalex.org/I3017902709"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055361262","display_name":"Muhammed Hasdemir","orcid":"https://orcid.org/0000-0001-5901-3699","observed_orcids":["https://orcid.org/0000-0001-5901-3699"]},"institutions":[{"id":"https://openalex.org/I76806599","display_name":"Adnan Menderes University","ror":"https://ror.org/03n7yzv56","country_code":"TR","type":"education","lineage":["https://openalex.org/I76806599"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Muhammed Hasdemir","raw_affiliation_strings":["Ayd\u0131n Vocational School of Health Services, Ayd\u0131n Adnan Menderes University, Ayd\u0131n, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ayd\u0131n Vocational School of Health Services, Ayd\u0131n Adnan Menderes University, Ayd\u0131n, Turkey","institution_ids":["https://openalex.org/I76806599"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055361262"],"corresponding_institution_ids":["https://openalex.org/I76806599"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.6586732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.7167999744415283,"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"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.7167999744415283,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.16380000114440918,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.07620000094175339,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/cauchy-problem","display_name":"Cauchy problem","score":0.9440000057220459},{"id":"https://openalex.org/keywords/unbounded-domains","display_name":"unbounded domains","score":0.8840000033378601},{"id":"https://openalex.org/keywords/uniqueness","display_name":"uniqueness","score":0.7590000033378601},{"id":"https://openalex.org/keywords/structure-preserving-numerical-methods","display_name":"structure-preserving numerical methods","score":0.7300000190734863},{"id":"https://openalex.org/keywords/crank-nicolson-method","display_name":"Crank-Nicolson scheme","score":0.9100000262260437},{"id":"https://openalex.org/keywords/unitary-evolution","display_name":"unitary evolution","score":0.7870000004768372}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7620999813079834},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5613999962806702},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4221000075340271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41690000891685486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38429999351501465},{"id":"https://openalex.org/C155940","wikidata":"https://www.wikidata.org/wiki/Q7886967","display_name":"Uniqueness theorem for Poisson's equation","level":3,"score":0.336899995803833},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30000001192092896},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1038/s41598-026-74137-8","doi":"https://doi.org/10.1038/s41598-026-74137-8","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-74137-8","pdf_url":"https://www.nature.com/articles/s41598-026-74137-8_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:7450637824b54c17a426472448df5217","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/7450637824b54c17a426472448df5217","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,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scientific Reports, Vol 16, Iss 1 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1038/s41598-026-74137-8","doi":"https://doi.org/10.1038/s41598-026-74137-8","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-74137-8","pdf_url":"https://www.nature.com/articles/s41598-026-74137-8_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","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/W7220838602.pdf","grobid_xml":"https://content.openalex.org/works/W7220838602.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1965940811","https://openalex.org/W1974577433","https://openalex.org/W2024905581","https://openalex.org/W2032246197","https://openalex.org/W2045816026","https://openalex.org/W2047227642","https://openalex.org/W2067199667","https://openalex.org/W2188921815","https://openalex.org/W2794845301","https://openalex.org/W2914513724","https://openalex.org/W2931033299","https://openalex.org/W2945696540","https://openalex.org/W2963810156","https://openalex.org/W3037211392","https://openalex.org/W4309562790","https://openalex.org/W4313126164","https://openalex.org/W4392522786","https://openalex.org/W4399055512","https://openalex.org/W4415551568"],"related_works":["https://openalex.org/W3037211392","https://openalex.org/W7212615557","https://openalex.org/W7133516197","https://openalex.org/W2039257330","https://openalex.org/W2609396150","https://openalex.org/W2047517169","https://openalex.org/W4297781084","https://openalex.org/W1976424722","https://openalex.org/W4223970227","https://openalex.org/W4399997681"],"abstract_inverted_index":{"In":[0,57],"this":[1],"paper,":[2],"we":[3],"investigate":[4],"a":[5,53,59],"Cauchy":[6,48],"problem":[7,49],"for":[8,45,67],"an":[9,15],"ultrahyperbolic":[10],"Schr\u00f6dinger":[11,19],"equation":[12],"posed":[13],"in":[14,22,29],"unbounded":[16],"domain.":[17],"Ultrahyperbolic":[18],"models":[20],"arise":[21],"multidimensional":[23],"wave":[24,31],"propagation":[25],"and":[26,39,84,99,103],"have":[27],"applications":[28],"water":[30],"theory,":[32,35],"quantum":[33],"kinetic":[34],"ferromagnetism,":[36],"nonlinear":[37],"optics,":[38],"plasma":[40],"physics.":[41],"A":[42],"uniqueness":[43],"result":[44],"the":[46,68,72,75,86,95,101,107],"considered":[47],"is":[50,65,82],"established":[51],"using":[52],"pointwise":[54],"Carleman":[55],"estimate.":[56],"addition,":[58],"second-order,":[60],"structure-preserving":[61],"Crank\u2013Nicolson":[62],"finite-difference":[63],"scheme":[64],"developed":[66],"numerical":[69,108],"solution":[70],"of":[71,97,106],"problem.":[73],"For":[74],"homogeneous":[76],"constant-coefficient":[77],"problem,":[78],"its":[79],"discrete":[80,87],"evolution":[81],"unitary":[83],"conserves":[85],"\\(\\ell":[88],"_{h}^{2}\\)":[89],"-norm":[90],"exactly.":[91],"Numerical":[92],"experiments":[93],"illustrate":[94],"behaviour":[96],"solutions":[98],"verify":[100],"accuracy":[102],"conservation":[104],"properties":[105],"scheme.":[109]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-08T00:00:00"}