{"id":"https://openalex.org/W7220378480","doi":"https://doi.org/10.48550/arxiv.2610.02747","title":"Lower regularity well-posedness for a higher-order Schr\u00f6dinger equation with cubic nonlinearities on the half-line","display_name":"Lower regularity well-posedness for a higher-order Schr\u00f6dinger equation with cubic nonlinearities on the half-line","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220378480","doi":"https://doi.org/10.48550/arxiv.2610.02747"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02747","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02747","pdf_url":"https://arxiv.org/pdf/2610.02747","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/2610.02747","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157424559","display_name":"Yuhao Xi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xi, Yuhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5157595019","display_name":"Shenghao Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Shenghao","raw_affiliation_strings":["School of Mathematical Sciences , University of Electronic Science and Technology of China , Chengdu , Sichuan 610054 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , University of Electronic Science and Technology of China , Chengdu , Sichuan 610054 , China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":1.0,"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":1.0,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0,"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"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.0,"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/higher-order-nonlinear-schrodinger-equation","display_name":"higher-order nonlinear Schr\u00f6dinger equation","score":0.9509999752044678},{"id":"https://openalex.org/keywords/kerr-nonlinearity","display_name":"Kerr nonlinearity","score":0.9539999961853027},{"id":"https://openalex.org/keywords/well-posedness","display_name":"well-posedness","score":0.8550000190734863},{"id":"https://openalex.org/keywords/trilinear-estimates","display_name":"trilinear estimates","score":0.8510000109672546},{"id":"https://openalex.org/keywords/strichartz-estimates","display_name":"Strichartz estimates","score":0.8880000114440918},{"id":"https://openalex.org/keywords/rays","display_name":"rays","score":0.8159999847412109},{"id":"https://openalex.org/keywords/resonance","display_name":"resonance","score":0.3880000114440918},{"id":"https://openalex.org/keywords/optimal-regularity","display_name":"optimal regularity","score":0.6269999742507935},{"id":"https://openalex.org/keywords/dispersive-partial-differential-equations","display_name":"dispersive equations","score":0.5630000233650208}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7728999853134155},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6449000239372253},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5821999907493591},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5791000127792358},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.5110999941825867},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4702000021934509},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.46459999680519104},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.397599995136261},{"id":"https://openalex.org/C108779253","wikidata":"https://www.wikidata.org/wiki/Q5282591","display_name":"Dispersive partial differential equation","level":3,"score":0.33640000224113464},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.27059999108314514}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02747","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02747","pdf_url":"https://arxiv.org/pdf/2610.02747","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.2610.02747","doi":"https://doi.org/10.48550/arxiv.2610.02747","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02747","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02747","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02747","pdf_url":"https://arxiv.org/pdf/2610.02747","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":[{"id":"https://openalex.org/G869107361","display_name":null,"funder_award_id":"12001084","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220378480.pdf","grobid_xml":"https://content.openalex.org/works/W7220378480.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2063814247","https://openalex.org/W7127568510","https://openalex.org/W3012111318","https://openalex.org/W4415122140","https://openalex.org/W4400025496","https://openalex.org/W4221162024","https://openalex.org/W2949223680","https://openalex.org/W2272608964","https://openalex.org/W2592457846","https://openalex.org/W4386603523"],"abstract_inverted_index":{"In":[0,92],"this":[1],"paper,":[2],"we":[3,96],"continue":[4],"the":[5,12,66,69,74,80,106,121,133],"study":[6],"of":[7,19,120,127],"Himonas":[8],"and":[9,22,62,84],"Yan\\cite{himonas2024schrodinger,himonas2026higher,himonas2024higher}":[10],"on":[11,68,125],"nonlinear":[13],"Schr\u00f6dinger":[14],"equation":[15],"with":[16],"a":[17,109],"dispersion":[18],"order":[20],"$2m$":[21],"cubic":[23],"nonlinearities,":[24],"\\[":[25],"iu_t+\\left(":[26],"-1":[27],"\\right)":[28,41,45,49,53],"^{m+1}\\partial":[29],"_{x}^{2m}u=N_k\\left(":[30],"u,u,u":[31,40,44,48,52],"\\right),":[32],"\\]":[33],"where,":[34],"$m\\ge1$":[35],"being":[36],"an":[37,86],"integer,":[38],"\\[N_0\\left(":[39],"=uuu,\\quad":[42],"N_1\\left(":[43],"=\\bar{u}uu,\\quad":[46],"N_2\\left(":[47],"=\\bar{u}\\bar{u}u,\\quad":[50],"N_3\\left(":[51],"=\\bar{u}\\bar{u}\\bar{u},\\]":[54],"We":[55],"derive":[56],"trilinear":[57,122],"estimates":[58,123],"at":[59,73,99],"lower":[60],"regularity":[61,76],"thereby":[63],"prove":[64],"that":[65],"cNLS-2m":[67],"half-line":[70],"is":[71],"well-posed":[72],"optimal":[75],"$s=-\\fr{m-1}{2}$.":[77],"This":[78],"improves":[79],"previous":[81],"result,":[82],"$s>-\\fr{m-1}{2}$,":[83],"answers":[85],"open":[87],"question":[88],"left":[89],"in":[90,138],"\\cite{himonas2026higher}.":[91,139],"addition,":[93],"for":[94,104,116],"$k=0,2$,":[95],"establish":[97],"well-posedness":[98,115],"$s=-\\fr{m-1}{2}$":[100],"as":[101],"well.":[102],"Moreover,":[103],"$k=3$,":[105],"nonlinearity":[107],"exhibits":[108],"stronger":[110],"resonance":[111],"relation,":[112],"which":[113,130],"implies":[114],"$s>-\\fr{2m-1}{3}$.":[117],"Our":[118],"derivation":[119],"relies":[124],"varieties":[126],"Strichartz":[128],"estimates,":[129],"differs":[131],"from":[132],"$[k;Z]$-multiplier":[134],"norm":[135],"method":[136],"employed":[137]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-06T00:00:00"}
