{"id":"https://openalex.org/W4221155707","doi":"https://doi.org/10.1007/s00332-022-09834-5","title":"Nanoptera in Higher-Order Nonlinear Schr\u00f6dinger Equations: Effects of Discretization","display_name":"Nanoptera in Higher-Order Nonlinear Schr\u00f6dinger Equations: Effects of Discretization","publication_year":2022,"publication_date":"2022-11-23","ids":{"openalex":"https://openalex.org/W4221155707","doi":"https://doi.org/10.1007/s00332-022-09834-5"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-022-09834-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-022-09834-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09834-5.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09834-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088659150","display_name":"Aaron J. Moston-Duggan","orcid":"https://orcid.org/0000-0003-1189-4065"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Aaron J. Moston-Duggan","raw_affiliation_strings":["School of Mathematical and Physical Sciences, Macquarie University, 12 Wally\u2019s Walk, Macquarie University, NSW, 2109, Australia"],"raw_orcid":"https://orcid.org/0000-0003-1189-4065","affiliations":[{"raw_affiliation_string":"School of Mathematical and Physical Sciences, Macquarie University, 12 Wally\u2019s Walk, Macquarie University, NSW, 2109, Australia","institution_ids":["https://openalex.org/I99043593"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058684689","display_name":"Mason A. Porter","orcid":"https://orcid.org/0000-0002-5166-0717"},"institutions":[{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]},{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mason A. Porter","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, 90095, USA","Santa Fe Institute, Santa Fe, NM, 87501, USA"],"raw_orcid":"https://orcid.org/0000-0002-5166-0717","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, 90095, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Santa Fe Institute, Santa Fe, NM, 87501, USA","institution_ids":["https://openalex.org/I1308548392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014200379","display_name":"Christopher J. Lustri","orcid":"https://orcid.org/0000-0001-9504-277X"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Christopher J. Lustri","raw_affiliation_strings":["School of Mathematical and Physical Sciences, Macquarie University, 12 Wally\u2019s Walk, Macquarie University, NSW, 2109, Australia"],"raw_orcid":"https://orcid.org/0000-0001-9504-277X","affiliations":[{"raw_affiliation_string":"School of Mathematical and Physical Sciences, Macquarie University, 12 Wally\u2019s Walk, Macquarie University, NSW, 2109, Australia","institution_ids":["https://openalex.org/I99043593"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088659150"],"corresponding_institution_ids":["https://openalex.org/I99043593"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0380874,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.8499000072479248,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.8499000072479248,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.09589999914169312,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.007199999876320362,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8370039463043213},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7024853825569153},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6438966989517212},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6272696256637573},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.610231876373291},{"id":"https://openalex.org/keywords/exponential-decay","display_name":"Exponential decay","score":0.5289202928543091},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4447668194770813},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.43444910645484924},{"id":"https://openalex.org/keywords/method-of-matched-asymptotic-expansions","display_name":"Method of matched asymptotic expansions","score":0.4290992319583893},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4162823557853699},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.25331318378448486},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24173927307128906},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06267273426055908}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8370039463043213},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7024853825569153},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6438966989517212},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6272696256637573},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.610231876373291},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.5289202928543091},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4447668194770813},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.43444910645484924},{"id":"https://openalex.org/C89407435","wikidata":"https://www.wikidata.org/wiki/Q17098224","display_name":"Method of matched asymptotic expansions","level":3,"score":0.4290992319583893},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4162823557853699},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.25331318378448486},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24173927307128906},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06267273426055908}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00332-022-09834-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-022-09834-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09834-5.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2203.08407","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2203.08407","pdf_url":"https://arxiv.org/pdf/2203.08407","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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.2203.08407","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2203.08407","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00332-022-09834-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-022-09834-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09834-5.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7902695234","display_name":null,"funder_award_id":"190101190","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4221155707.pdf","grobid_xml":"https://content.openalex.org/works/W4221155707.grobid-xml"},"referenced_works_count":74,"referenced_works":["https://openalex.org/W71629980","https://openalex.org/W190947673","https://openalex.org/W649794155","https://openalex.org/W1533185225","https://openalex.org/W1599623497","https://openalex.org/W1971892010","https://openalex.org/W1972140872","https://openalex.org/W1974753876","https://openalex.org/W1979386794","https://openalex.org/W1983031318","https://openalex.org/W1983034410","https://openalex.org/W1983877794","https://openalex.org/W1985506570","https://openalex.org/W1987327779","https://openalex.org/W1994520194","https://openalex.org/W1995346591","https://openalex.org/W2003735705","https://openalex.org/W2020698291","https://openalex.org/W2022442936","https://openalex.org/W2022591585","https://openalex.org/W2024067576","https://openalex.org/W2024717204","https://openalex.org/W2024975835","https://openalex.org/W2032330793","https://openalex.org/W2032377644","https://openalex.org/W2039513402","https://openalex.org/W2040013140","https://openalex.org/W2047148634","https://openalex.org/W2047404392","https://openalex.org/W2048275247","https://openalex.org/W2052343776","https://openalex.org/W2059056989","https://openalex.org/W2062345443","https://openalex.org/W2063560842","https://openalex.org/W2067402298","https://openalex.org/W2067534352","https://openalex.org/W2068176034","https://openalex.org/W2069098156","https://openalex.org/W2069226291","https://openalex.org/W2069942719","https://openalex.org/W2070666175","https://openalex.org/W2070691428","https://openalex.org/W2079762605","https://openalex.org/W2084480849","https://openalex.org/W2087208877","https://openalex.org/W2088415519","https://openalex.org/W2088974619","https://openalex.org/W2105858085","https://openalex.org/W2112030201","https://openalex.org/W2112645274","https://openalex.org/W2115890772","https://openalex.org/W2136989908","https://openalex.org/W2139131426","https://openalex.org/W2155912913","https://openalex.org/W2162263411","https://openalex.org/W2340547177","https://openalex.org/W2490792505","https://openalex.org/W2593064165","https://openalex.org/W2893257945","https://openalex.org/W2951562542","https://openalex.org/W2964145016","https://openalex.org/W2981827678","https://openalex.org/W2982006093","https://openalex.org/W2990429958","https://openalex.org/W3015524350","https://openalex.org/W3027813957","https://openalex.org/W3131767918","https://openalex.org/W3140105605","https://openalex.org/W3199435061","https://openalex.org/W3203120128","https://openalex.org/W3214944642","https://openalex.org/W4210544878","https://openalex.org/W4229074591","https://openalex.org/W4234743066"],"related_works":["https://openalex.org/W62743517","https://openalex.org/W61100852","https://openalex.org/W821957","https://openalex.org/W73536336","https://openalex.org/W51096756","https://openalex.org/W39222330","https://openalex.org/W24104221","https://openalex.org/W65708507","https://openalex.org/W29695857","https://openalex.org/W4629307"],"abstract_inverted_index":{"Abstract":[0],"We":[1,70,84,158],"consider":[2],"generalizations":[3],"of":[4,30,43,89,182,190],"nonlinear":[5],"Schr\u00f6dinger":[6],"equations,":[7],"which":[8,46,118,166],"we":[9,119,139,195],"call":[10],"\u201cKarpman":[11],"equations,\u201d":[12],"that":[13,64,141,161,197],"include":[14],"additional":[15],"linear":[16],"higher-order":[17,188],"derivatives.":[18],"Singularly-perturbed":[19],"Karpman":[20,60,82,100,112,131,193,218],"equations":[21,61,101,132],"produce":[22],"generalized":[23],"solitary":[24,31],"waves":[25,32],"(GSWs)":[26],"in":[27,45,67,79,128,135,147,152,214],"the":[28,47,87,142,148,153,162,180,191,198,215],"form":[29],"with":[33,133],"exponentially":[34],"small":[35],"oscillatory":[36,48,176],"tails.":[37],"Nanoptera":[38],"are":[39],"a":[40,95,110,169,203],"special":[41],"type":[42],"GSW":[44],"tails":[49,150],"do":[50],"not":[51],"decay.":[52],"Previous":[53],"research":[54],"on":[55,91,179],"continuous":[56,81,99,111,137,154,217],"third-order":[57],"and":[58,102,145,155,174],"fourth-order":[59,192],"has":[62],"shown":[63],"nanoptera":[65,78,92,127,134,149],"occur":[66],"specific":[68],"settings.":[69],"use":[71],"exponential":[72,122],"asymptotic":[73,123],"techniques":[74],"to":[75,98,202,211],"identify":[76],"traveling":[77],"singularly-perturbed":[80],"equations.":[83,157],"then":[85],"study":[86,120],"effect":[88],"discretization":[90,97,108],"by":[93,185],"applying":[94],"finite-difference":[96,107],"examining":[103],"traveling-wave":[104],"solutions.":[105],"The":[106],"turns":[109],"equation":[113],"into":[114],"an":[115],"advance\u2013delay":[116],"equation,":[117,194],"using":[121],"analysis.":[124],"By":[125],"comparing":[126,186],"these":[129],"discrete":[130,156],"their":[136],"counterparts,":[138],"show":[140,160,196],"oscillation":[143],"amplitudes":[144],"periods":[146],"differ":[151],"also":[159],"parameter":[163],"values":[164],"at":[165],"there":[167],"is":[168],"bifurcation":[170,199],"between":[171],"nanopteron":[172],"solutions":[173,177],"decaying":[175],"depends":[178],"choice":[181],"discretization.":[183],"Finally,":[184],"different":[187],"discretizations":[189],"value":[200],"tends":[201],"nonzero":[204],"constant":[205],"for":[206],"large":[207],"orders,":[208],"rather":[209],"than":[210],"0":[212],"as":[213],"associated":[216],"equation.":[219]},"counts_by_year":[],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2022-04-03T00:00:00"}
