{"id":"https://openalex.org/W7160096047","doi":"https://doi.org/10.48550/arxiv.2605.00484","title":"Almost global large deviations principle for the KdV equation","display_name":"Almost global large deviations principle for the KdV equation","publication_year":2026,"publication_date":"2026-05-01","ids":{"openalex":"https://openalex.org/W7160096047","doi":"https://doi.org/10.48550/arxiv.2605.00484"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2605.00484","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.00484","pdf_url":"https://arxiv.org/pdf/2605.00484","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2605.00484","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135259672","display_name":"Riccardo Berforini D'Aquino","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"D'Aquino, Riccardo Berforini","raw_affiliation_strings":["International School for Advanced Studies (SISSA) , Via Bonomea 265 , 34136 , Trieste , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International School for Advanced Studies (SISSA) , Via Bonomea 265 , 34136 , Trieste , Italy","institution_ids":["https://openalex.org/I138549579"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009530856","display_name":"Ricardo Grande","orcid":"https://orcid.org/0000-0002-1521-6790","observed_orcids":["https://orcid.org/0000-0002-1521-6790"]},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Grande, Ricardo","raw_affiliation_strings":["International School for Advanced Studies (SISSA) , Via Bonomea 265 , 34136 , Trieste , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International School for Advanced Studies (SISSA) , Via Bonomea 265 , 34136 , Trieste , Italy","institution_ids":["https://openalex.org/I138549579"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I138549579"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9951000213623047,"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":0.9951000213623047,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.00419999985024333,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kdv-equation","display_name":"Korteweg-de Vries equation","score":0.9750000238418579},{"id":"https://openalex.org/keywords/large-deviations-principle","display_name":"large deviations principle","score":0.9670000076293945},{"id":"https://openalex.org/keywords/extreme-waves","display_name":"extreme waves","score":0.7799999713897705},{"id":"https://openalex.org/keywords/random-initial-data","display_name":"random initial data","score":0.9089999794960022},{"id":"https://openalex.org/keywords/invariant-tori","display_name":"invariant tori","score":0.7590000033378601},{"id":"https://openalex.org/keywords/coherent-structures","display_name":"coherent structures","score":0.8159999847412109},{"id":"https://openalex.org/keywords/birkhoff-normal-form","display_name":"Birkhoff normal form","score":0.9520000219345093},{"id":"https://openalex.org/keywords/integrable-systems","display_name":"integrable systems","score":0.6629999876022339},{"id":"https://openalex.org/keywords/long-time-behavior","display_name":"long-time behavior","score":0.5},{"id":"https://openalex.org/keywords/weakly-nonlinear-regime","display_name":"weakly nonlinear regime","score":0.6620000004768372}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.6794999837875366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6729999780654907},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.641700029373169},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.6036999821662903},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5730999708175659},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.5109999775886536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4893999993801117},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4729999899864197},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4357999861240387},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.41589999198913574},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4092999994754791},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.39469999074935913},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.38519999384880066},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3765999972820282},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.35600000619888306},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.3495999872684479},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.3474999964237213},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.3325999975204468},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C4188701","wikidata":"https://www.wikidata.org/wiki/Q5282585","display_name":"Dispersionless equation","level":5,"score":0.28630000352859497},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2791000008583069},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.25870001316070557},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2524000108242035},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2605.00484","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.00484","pdf_url":"https://arxiv.org/pdf/2605.00484","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05773748v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-05773748v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2605.00484","doi":"https://doi.org/10.48550/arxiv.2605.00484","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.00484","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2605.00484","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.00484","pdf_url":"https://arxiv.org/pdf/2605.00484","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7160096047.pdf","grobid_xml":"https://content.openalex.org/works/W7160096047.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4415871180","https://openalex.org/W7111188605"],"related_works":["https://openalex.org/W7213981723","https://openalex.org/W2620187801","https://openalex.org/W4416340346","https://openalex.org/W4387616466","https://openalex.org/W3209684556","https://openalex.org/W2286860821","https://openalex.org/W7155057706","https://openalex.org/W4415871180","https://openalex.org/W3004993110","https://openalex.org/W36042086"],"abstract_inverted_index":{"We":[0,21,110],"study":[1],"extreme":[2,80],"wave":[3,81],"formation":[4,82],"for":[5,27,41,79],"the":[6,11,28,31,49,53,64,105,113,118,134,137,142],"Korteweg-de":[7],"Vries":[8],"equation":[9],"on":[10,67,84],"torus":[12],"with":[13,130],"random":[14],"initial":[15],"data":[16],"of":[17,30,52,55,107,136,144],"average":[18],"size":[19],"$\u03b5$.":[20],"establish":[22],"a":[23,89,125],"large":[24,58,91],"deviations":[25],"principle":[26],"supremum":[29],"solution":[32],"over":[33,147],"arbitrarily":[34],"long":[35,148],"polynomial":[36],"timescales":[37],"$t":[38],"\\leq":[39],"\u03b5^{-n}$":[40],"any":[42],"fixed":[43],"natural":[44],"number":[45],"$n$.":[46],"This":[47],"identifies":[48],"leading-order":[50],"asymptotics":[51],"probability":[54,143],"observing":[56],"unusually":[57],"amplitudes.":[59],"In":[60],"this":[61],"integrable":[62,138],"setting,":[63],"dynamics":[65,139],"evolves":[66],"invariant":[68],"tori":[69],"where":[70],"Fourier":[71],"moduli":[72],"are":[73],"almost":[74],"conserved,":[75],"ruling":[76],"out":[77],"mechanisms":[78],"based":[83],"resonant":[85],"energy":[86],"exchange.":[87],"As":[88],"result,":[90],"amplitudes":[92],"can":[93],"only":[94],"arise":[95],"through":[96],"coherent":[97],"structures":[98],"or":[99],"dispersive":[100],"focusing,":[101],"which":[102],"corresponds":[103],"to":[104,140],"quasi-synchronization":[106,146],"many":[108],"phases.":[109],"show":[111],"that":[112],"latter":[114],"is":[115],"dominant":[116],"in":[117],"weakly":[119],"nonlinear":[120],"regime.":[121],"Our":[122],"approach":[123],"combines":[124],"Birkhoff":[126],"normal":[127],"form":[128],"analysis":[129],"probabilistic":[131],"arguments,":[132],"exploiting":[133],"stability":[135],"control":[141],"phase":[145],"timescales.":[149]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-05-05T00:00:00"}