{"id":"https://openalex.org/W7224128276","doi":"https://doi.org/10.48550/arxiv.2610.37183","title":"The focusing coupled nonlinear Schr\u00f6dinger equation with parallel nonzero boundary conditions: long--time asmptotics","display_name":"The focusing coupled nonlinear Schr\u00f6dinger equation with parallel nonzero boundary conditions: long--time asmptotics","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224128276","doi":"https://doi.org/10.48550/arxiv.2610.37183"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.37183","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37183","pdf_url":"https://arxiv.org/pdf/2610.37183","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.37183","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130227158","display_name":"Haibing Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Haibing","raw_affiliation_strings":["\ud835\udc4e School of Mathematics and Statistics , Zhengzhou University , 100 Kexue Road , Zhengzhou , Henan 450001 , People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\ud835\udc4e School of Mathematics and Statistics , Zhengzhou University , 100 Kexue Road , Zhengzhou , Henan 450001 , People's Republic of China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066890510","display_name":"Xianguo Geng","orcid":"https://orcid.org/0000-0003-2980-7660","observed_orcids":["https://orcid.org/0000-0003-2980-7660"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Geng, Xianguo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021221660","display_name":"\u859b\u6ce2","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xue, Bo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091881046","display_name":"Minxin Jia","orcid":"https://orcid.org/0000-0002-1886-3512","observed_orcids":["https://orcid.org/0000-0002-1886-3512"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jia, Minxin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.8525000214576721,"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":0.8525000214576721,"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":0.14030000567436218,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.0005000000237487257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/long-time-behavior","display_name":"long-time behavior","score":0.8560000061988831},{"id":"https://openalex.org/keywords/riemann-hilbert-problem","display_name":"Riemann-Hilbert problem","score":0.847000002861023},{"id":"https://openalex.org/keywords/deift-zhou-nonlinear-steepest-descent","display_name":"Deift-Zhou nonlinear steepest descent","score":0.8560000061988831},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.6940000057220459}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6032999753952026},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5580000281333923},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5386999845504761},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.46779999136924744},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46630001068115234},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.46149998903274536},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4611000120639801},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.460099995136261},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4438999891281128},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44110000133514404},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4336000084877014},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.33629998564720154},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2897999882698059},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.25110000371932983},{"id":"https://openalex.org/C174256460","wikidata":"https://www.wikidata.org/wiki/Q911364","display_name":"Perturbation theory (quantum mechanics)","level":2,"score":0.250900000333786},{"id":"https://openalex.org/C89407435","wikidata":"https://www.wikidata.org/wiki/Q17098224","display_name":"Method of matched asymptotic expansions","level":3,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.37183","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37183","pdf_url":"https://arxiv.org/pdf/2610.37183","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.2610.37183","doi":"https://doi.org/10.48550/arxiv.2610.37183","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.37183","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:2610.37183","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37183","pdf_url":"https://arxiv.org/pdf/2610.37183","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/W7224128276.pdf","grobid_xml":"https://content.openalex.org/works/W7224128276.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2283798083","https://openalex.org/W7166700469","https://openalex.org/W3012083171","https://openalex.org/W2944116731","https://openalex.org/W4285095225","https://openalex.org/W2769861550","https://openalex.org/W4287772943","https://openalex.org/W4285167441","https://openalex.org/W7155189884","https://openalex.org/W2023921325"],"abstract_inverted_index":{"We":[0,24],"study":[1],"the":[2,8,21,45,50,73,75,83,89,92,104,108,111,115,123,127,146,157],"long-time":[3],"behavior":[4],"of":[5,7,28,110],"solutions":[6],"focusing":[9],"coupled":[10],"nonlinear":[11,148],"Schr\u00f6dinger":[12],"equations":[13],"with":[14,54,122,152],"parallel":[15,69,81,133],"constant":[16],"nonzero":[17],"boundary":[18],"conditions":[19],"in":[20,88],"solitonless":[22],"setting.":[23],"distinguish":[25],"three":[26],"types":[27],"asymptotic":[29,47,77],"regions:":[30],"plane-wave":[31],"regions,":[32,35,91],"modulated":[33,100],"elliptic-wave":[34,90],"and":[36,49,70],"Painlev\u00e9-II":[37],"transition":[38],"regions.":[39],"In":[40,86],"each":[41],"region,":[42],"we":[43],"derive":[44],"leading":[46,76,93],"term":[48,78],"first":[51],"correction,":[52],"together":[53,151],"explicit":[55],"error":[56],"bounds.":[57],"Our":[58],"results":[59],"show":[60],"that,":[61],"although":[62],"localized":[63],"perturbations":[64,134],"may":[65],"have":[66],"components":[67],"both":[68],"orthogonal":[71,113,138],"to":[72,82,114,132,137,156],"background,":[74],"is":[79,95,117,120,129,142],"always":[80],"background":[84,105,116,128],"vector.":[85],"particularly,":[87],"order":[94],"given":[96],"by":[97],"a":[98,153],"scalar":[99],"elliptic":[101],"wave":[102],"multiplying":[103],"vector,":[106],"while":[107],"component":[109],"solution":[112],"\\(O(t^{-1/2})\\).":[118],"This":[119],"consistent":[121],"linear":[124],"stability":[125],"analysis:":[126],"modulationally":[130],"unstable":[131],"but":[135],"stable":[136],"perturbations.":[139],"The":[140],"proof":[141],"based":[143],"on":[144],"applying":[145],"Deift--Zhou":[147],"steepest-descent":[149],"method,":[150],"\\(G\\)-function":[154],"mechanism,":[155],"associated":[158],"\\(3\\times3\\)":[159],"Riemann--Hilbert":[160],"problem.":[161]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-29T00:00:00"}