{"id":"https://openalex.org/W7221048848","doi":"https://doi.org/10.48550/arxiv.2610.07797","title":"The emergence of rapid oscillations in a fifth-order KdV equation","display_name":"The emergence of rapid oscillations in a fifth-order KdV equation","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7221048848","doi":"https://doi.org/10.48550/arxiv.2610.07797"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07797","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07797","pdf_url":"https://arxiv.org/pdf/2610.07797","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":null,"license_id":null,"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/2610.07797","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014200379","display_name":"Christopher J. Lustri","orcid":"https://orcid.org/0000-0001-9504-277X","observed_orcids":["https://orcid.org/0000-0001-9504-277X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lustri, Christopher J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081545907","display_name":"Stephen Jonathan Chapman","orcid":"https://orcid.org/0000-0003-3347-6024","observed_orcids":["https://orcid.org/0000-0003-3347-6024"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Chapman, S. Jonathan","raw_affiliation_strings":["Mathematical Institute , University of Oxford , Andrew Wiles Building , Radcliffe Observatory Quarter , Woodstock Road , Oxford OX2 6GG , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute , University of Oxford , Andrew Wiles Building , Radcliffe Observatory Quarter , Woodstock Road , Oxford OX2 6GG , UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157947266","display_name":"Richard C. P. Nicotra","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Nicotra, Richard C. P.","raw_affiliation_strings":["School of Mathematics and Statistics , The University of Sydney , NSW 2006 , Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , The University of Sydney , NSW 2006 , Australia","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.8295999765396118,"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":0.8295999765396118,"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":0.09600000083446503,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.051500000059604645,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fifth-order-korteweg-de-vries-equation","display_name":"fifth-order Korteweg-de Vries equation","score":0.9539999961853027},{"id":"https://openalex.org/keywords/stokes-phenomenon","display_name":"Stokes phenomenon","score":0.8389999866485596},{"id":"https://openalex.org/keywords/exponential-asymptotics","display_name":"exponential asymptotics","score":0.703000009059906},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"gradient descent","score":0.8149999976158142}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.707099974155426},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6263999938964844},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6195999979972839},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6129000186920166},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6119999885559082},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5259000062942505},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.49309998750686646},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4821999967098236},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.47119998931884766},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.45329999923706055},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4487999975681305},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C158847443","wikidata":"https://www.wikidata.org/wiki/Q1997812","display_name":"Method of steepest descent","level":2,"score":0.39410001039505005},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.38280001282691956},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.32089999318122864},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3059999942779541},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2872999906539917},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C66908091","wikidata":"https://www.wikidata.org/wiki/Q1127660","display_name":"Damped wave","level":3,"score":0.26750001311302185},{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C89407435","wikidata":"https://www.wikidata.org/wiki/Q17098224","display_name":"Method of matched asymptotic expansions","level":3,"score":0.2628999948501587},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.26109999418258667}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07797","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07797","pdf_url":"https://arxiv.org/pdf/2610.07797","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.07797","doi":"https://doi.org/10.48550/arxiv.2610.07797","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07797","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:2610.07797","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07797","pdf_url":"https://arxiv.org/pdf/2610.07797","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":null,"license_id":null,"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/W7221048848.pdf","grobid_xml":"https://content.openalex.org/works/W7221048848.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W37834841","https://openalex.org/W190947673","https://openalex.org/W1490180844","https://openalex.org/W1967528517","https://openalex.org/W1972643483","https://openalex.org/W1978043962","https://openalex.org/W1983031318","https://openalex.org/W1987052298","https://openalex.org/W1998371978","https://openalex.org/W2026515283","https://openalex.org/W2039513402","https://openalex.org/W2047148634","https://openalex.org/W2056235746","https://openalex.org/W2070666175","https://openalex.org/W2113296719","https://openalex.org/W2118548772","https://openalex.org/W2128216632","https://openalex.org/W2128968062","https://openalex.org/W2129300940","https://openalex.org/W2147057598","https://openalex.org/W2150588152","https://openalex.org/W2162158201","https://openalex.org/W2169597393","https://openalex.org/W2333421954","https://openalex.org/W2549606326","https://openalex.org/W2785880153","https://openalex.org/W2943271495","https://openalex.org/W3209882192","https://openalex.org/W4237351959","https://openalex.org/W4304943839","https://openalex.org/W4390230156","https://openalex.org/W4408312281","https://openalex.org/W4416065843"],"related_works":["https://openalex.org/W2032741615","https://openalex.org/W190947673","https://openalex.org/W2047148634","https://openalex.org/W2067768315","https://openalex.org/W2608199703","https://openalex.org/W2906438842","https://openalex.org/W4405262280","https://openalex.org/W4400503096","https://openalex.org/W4405622680","https://openalex.org/W2588122558"],"abstract_inverted_index":{"We":[0,34],"consider":[1],"the":[2,11,36,49,61,66,72,79,84,87,107,115,142,163,176,181],"emergence":[3],"of":[4,65,74,86,106,166],"rapidly":[5],"propagating,":[6],"exponentially":[7],"small-amplitude":[8],"oscillations":[9,168],"in":[10,29,38,175,201],"impulsively":[12],"started":[13],"fifth-order":[14],"Korteweg--de":[15],"Vries":[16],"equation":[17],"(KdV5),":[18],"and":[19,40,54,83,109,127,169,179,188],"demonstrate":[20],"that":[21,47,119,192],"these":[22,93],"waves":[23],"originate":[24],"due":[25],"to":[26,77,112,141],"Stokes'":[27],"phenomenon":[28],"a":[30,96,197,202,207],"small-time":[31],"boundary":[32,204],"layer.":[33],"rescale":[35],"problem":[37],"time":[39],"construct":[41],"an":[42],"auxiliary":[43,67],"linear":[44],"PDE":[45,68],"(lKdV5)":[46],"reproduces":[48],"relevant":[50,80],"exponential":[51,124],"asymptotic":[52,81,117,125],"structure,":[53],"proceed":[55],"by":[56,123],"two":[57],"main":[58],"methods.":[59,153],"Firstly,":[60],"Fourier":[62],"transform":[63],"solution":[64],"is":[69,120,128,138,206],"analysed":[70],"via":[71],"method":[73],"steepest":[75,151],"descents":[76],"extract":[78],"contributions":[82],"locations":[85],"Stokes":[88,183,190,199],"curves.":[89],"Secondly,":[90],"we":[91,103],"reproduce":[92],"results":[94,155],"using":[95,150],"direct":[97],"factorial-over-power":[98,136],"analysis.":[99],"In":[100],"this":[101],"analysis,":[102],"make":[104],"use":[105],"initial":[108],"far-field":[110],"conditions":[111],"avoid":[113],"performing":[114],"local":[116],"matching":[118],"typically":[121],"required":[122],"methods":[126],"frequently":[129],"impossible":[130],"for":[131],"nonlinear":[132,144],"PDEs.":[133],"A":[134],"similar":[135],"analysis":[137],"then":[139],"applied":[140],"full":[143],"PDE,":[145],"which":[146],"cannot":[147],"be":[148],"studied":[149],"descent":[152],"The":[154],"agree":[156],"well":[157],"with":[158],"numerical":[159],"simulations,":[160],"demonstrating":[161],"both":[162,186],"rapid":[164],"propagation":[165],"non-decaying":[167],"transient":[170],"ripples":[171],"whose":[172],"amplitudes":[173],"decay":[174],"far":[177],"field,":[178],"revealing":[180],"complex":[182,198],"structure":[184,200],"(including":[185],"normal":[187],"higher-order":[189],"curves)":[191],"governs":[193],"their":[194],"emergence.":[195],"Such":[196],"temporal":[203],"layer":[205],"novel":[208],"phenomenon.":[209]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}