{"id":"https://openalex.org/W7220440174","doi":"https://doi.org/10.48550/arxiv.2610.02541","title":"Persistence of kinks in the NLS equation with competing nonlinearities","display_name":"Persistence of kinks in the NLS equation with competing nonlinearities","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220440174","doi":"https://doi.org/10.48550/arxiv.2610.02541"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02541","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02541","pdf_url":"https://arxiv.org/pdf/2610.02541","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/2610.02541","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113813532","display_name":"P. G. Kevrekidis","orcid":"https://orcid.org/0000-0002-7714-3689","observed_orcids":["https://orcid.org/0000-0002-7714-3689"]},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]},{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Kevrekidis, P. G.","raw_affiliation_strings":["Department of Mathematics and Statistics , McMaster University , Hamil- ton , Ontario , Canada , L8S 4K1","Department of Physics , University of Massachusetts Amherst , Amherst , MA 01003 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , McMaster University , Hamil- ton , Ontario , Canada , L8S 4K1","institution_ids":["https://openalex.org/I98251732"]},{"raw_affiliation_string":"Department of Physics , University of Massachusetts Amherst , Amherst , MA 01003 , USA","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5132911405","display_name":"D. E. Pelinovsky","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pelinovsky, D. E.","raw_affiliation_strings":["Department of Physics , University of Massachusetts Amherst , Amherst , MA 01003 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , University of Massachusetts Amherst , Amherst , MA 01003 , USA","institution_ids":["https://openalex.org/I24603500"]}]}],"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9750999808311462,"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":0.9750999808311462,"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":0.012900000438094139,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0071000000461936,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-schrodinger-equation","display_name":"nonlinear Schr\u00f6dinger equation","score":0.9850000143051147},{"id":"https://openalex.org/keywords/competing-nonlinearities","display_name":"competing nonlinearities","score":0.9860000014305115},{"id":"https://openalex.org/keywords/cubic-quintic-nonlinearity","display_name":"cubic-quintic nonlinearity","score":0.921999990940094},{"id":"https://openalex.org/keywords/external-potential","display_name":"external potential","score":0.6150000095367432},{"id":"https://openalex.org/keywords/standing-waves","display_name":"standing waves","score":0.6589999794960022},{"id":"https://openalex.org/keywords/lyapunov-schmidt-reduction","display_name":"Lyapunov-Schmidt reduction","score":0.9729999899864197},{"id":"https://openalex.org/keywords/effective-potential","display_name":"effective potential","score":0.921999990940094},{"id":"https://openalex.org/keywords/spectral-stability","display_name":"spectral stability","score":0.5139999985694885},{"id":"https://openalex.org/keywords/unstable-eigenvalues","display_name":"unstable eigenvalues","score":0.7049999833106995},{"id":"https://openalex.org/keywords/parity-breaking","display_name":"parity symmetry breaking","score":0.8849999904632568},{"id":"https://openalex.org/keywords/linearized-operator","display_name":"linearized operator","score":0.44200000166893005}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7462000250816345},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.7199000120162964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6104000210762024},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5863999724388123},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5329999923706055},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4765999913215637},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46939998865127563},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C80845027","wikidata":"https://www.wikidata.org/wiki/Q15144062","display_name":"Continuous spectrum","level":2,"score":0.41350001096725464},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4090000092983246},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.40560001134872437},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.37470000982284546},{"id":"https://openalex.org/C124966035","wikidata":"https://www.wikidata.org/wiki/Q33104507","display_name":"Quintic function","level":3,"score":0.3709000051021576},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.36500000953674316},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3433000147342682},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3422999978065491},{"id":"https://openalex.org/C66908091","wikidata":"https://www.wikidata.org/wiki/Q1127660","display_name":"Damped wave","level":3,"score":0.323199987411499},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.32010000944137573},{"id":"https://openalex.org/C2780297109","wikidata":"https://www.wikidata.org/wiki/Q917390","display_name":"Essential spectrum","level":3,"score":0.31769999861717224},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.3109000027179718},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.30959999561309814},{"id":"https://openalex.org/C174256460","wikidata":"https://www.wikidata.org/wiki/Q911364","display_name":"Perturbation theory (quantum mechanics)","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C84229","wikidata":"https://www.wikidata.org/wiki/Q2116709","display_name":"Translational symmetry","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C71914180","wikidata":"https://www.wikidata.org/wiki/Q1071013","display_name":"Conserved quantity","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.2556999921798706}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02541","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02541","pdf_url":"https://arxiv.org/pdf/2610.02541","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.2610.02541","doi":"https://doi.org/10.48550/arxiv.2610.02541","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02541","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:2610.02541","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02541","pdf_url":"https://arxiv.org/pdf/2610.02541","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220440174.pdf","grobid_xml":"https://content.openalex.org/works/W7220440174.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7114802758","https://openalex.org/W7171831304"],"related_works":["https://openalex.org/W7114802758","https://openalex.org/W2033851598","https://openalex.org/W2093965803","https://openalex.org/W7098198027","https://openalex.org/W1971419845","https://openalex.org/W2979902444","https://openalex.org/W3020383650","https://openalex.org/W7054733900","https://openalex.org/W1992737652","https://openalex.org/W2025735959"],"abstract_inverted_index":{"External":[0],"potentials":[1],"break":[2],"the":[3,30,37,57,61,78,83,88,93,110,118,129,133,139,145,149,156,165,178,187,191],"translational":[4,79],"invariance":[5],"of":[6,17,33,60,68,82,95,100,128,148,158,186],"nonlinear":[7],"Schr\u00f6dinger":[8],"(NLS)":[9],"equations":[10],"and":[11,44,90,102,182],"generally":[12],"convert":[13],"a":[14,34,114,122],"continuous":[15,146],"family":[16],"standing":[18],"wave":[19],"solutions":[20],"into":[21],"isolated":[22],"pinned":[23,62],"states.":[24],"We":[25,74,105],"study":[26],"this":[27],"mechanism":[28],"for":[29,132,194],"prototypical":[31],"case":[32],"kink":[35],"in":[36,144],"NLS":[38],"equation":[39],"with":[40,174],"competing":[41],"focusing":[42],"cubic":[43],"defocusing":[45],"quintic":[46],"nonlinearities.":[47],"The":[48,126],"Lyapunov--Schmidt":[49],"reduction":[50],"method":[51],"is":[52,64,136,142,168],"used":[53],"to":[54,177],"prove":[55,91],"that":[56,92,108,155],"location":[58],"$s_0$":[59],"kinks":[63,159],"selected":[65],"near":[66],"roots":[67],"an":[69],"effective":[70],"potential":[71,167],"$V_{\\rm":[72,96],"eff}(s)$.":[73],"then":[75,117],"determine":[76],"how":[77],"zero":[80,140],"eigenvalue":[81,135,141],"Jacobian":[84,111],"operator":[85,112],"splits":[86],"under":[87],"perturbation":[89],"sign":[94],"eff}'(s_0)$":[97],"distinguishes":[98],"eigendirections":[99],"positive":[101],"negative":[103,115],"energy.":[104],"further":[106],"show":[107,154],"if":[109,164],"admits":[113],"eigenvalue,":[116],"stability":[119],"problem":[120],"contains":[121],"real":[123],"unstable":[124,134],"eigenvalue.":[125],"derivation":[127],"asymptotic":[130],"expansion":[131],"nonstandard":[137],"because":[138],"embedded":[143],"spectrum":[147],"linearized":[150],"operator.":[151],"Finally,":[152],"we":[153],"persistence":[157],"lacks":[160],"parity":[161],"symmetry":[162],"even":[163],"external":[166],"odd.":[169],"Numerical":[170],"continuation,":[171],"spectral":[172],"computations":[173],"domains":[175],"adapted":[176],"slowly":[179],"decaying":[180],"eigenfunctions,":[181],"direct":[183],"dynamical":[184],"simulations":[185],"time":[188],"evolution":[189],"corroborate":[190],"analytical":[192],"predictions":[193],"different":[195],"representative":[196],"examples.":[197]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}