{"id":"https://openalex.org/W4405046151","doi":"https://doi.org/10.1016/j.padiff.2024.101014","title":"On matrix Lax representations and constructions of Miura-type transformations for differential\u2013difference equations","display_name":"On matrix Lax representations and constructions of Miura-type transformations for differential\u2013difference equations","publication_year":2024,"publication_date":"2024-12-05","ids":{"openalex":"https://openalex.org/W4405046151","doi":"https://doi.org/10.1016/j.padiff.2024.101014"},"language":"en","primary_location":{"id":"doi:10.1016/j.padiff.2024.101014","doi":"https://doi.org/10.1016/j.padiff.2024.101014","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.padiff.2024.101014","pdf_url":null,"source":{"id":"https://openalex.org/S4210214501","display_name":"Partial Differential Equations in Applied Mathematics","issn_l":"2666-8181","issn":["2666-8181"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Partial Differential Equations in Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1016/j.padiff.2024.101014","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114438979","display_name":"Evgeny Chistov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I198371094","display_name":"Yaroslavl State University","ror":"https://ror.org/044s2fj67","country_code":"RU","type":"education","lineage":["https://openalex.org/I198371094"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Evgeny Chistov","raw_affiliation_strings":["Center of Integrable Systems, P.G. Demidov Yaroslavl State University, Yaroslavl, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center of Integrable Systems, P.G. Demidov Yaroslavl State University, Yaroslavl, Russia","institution_ids":["https://openalex.org/I198371094"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047274260","display_name":"Sergei Igonin","orcid":"https://orcid.org/0000-0002-2066-0490","observed_orcids":["https://orcid.org/0000-0002-2066-0490"]},"institutions":[{"id":"https://openalex.org/I198371094","display_name":"Yaroslavl State University","ror":"https://ror.org/044s2fj67","country_code":"RU","type":"education","lineage":["https://openalex.org/I198371094"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Sergei Igonin","raw_affiliation_strings":["Center of Integrable Systems, P.G. Demidov Yaroslavl State University, Yaroslavl, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center of Integrable Systems, P.G. Demidov Yaroslavl State University, Yaroslavl, Russia","institution_ids":["https://openalex.org/I198371094"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5114438979"],"corresponding_institution_ids":["https://openalex.org/I198371094"],"apc_list":{"value":1230,"currency":"USD","value_usd":1230},"apc_paid":{"value":1230,"currency":"USD","value_usd":1230},"fwci":0.4612,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.48089873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":null,"first_page":"101014","last_page":"101014"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9990000128746033,"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":0.9990000128746033,"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":0.0003000000142492354,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/differential-difference-equations","display_name":"differential-difference equations","score":0.8809999823570251},{"id":"https://openalex.org/keywords/gauge-transformations","display_name":"gauge transformations","score":0.8410000205039978},{"id":"https://openalex.org/keywords/integrable-systems","display_name":"integrable systems","score":0.8529999852180481},{"id":"https://openalex.org/keywords/toda-lattice","display_name":"Toda lattice","score":0.9639999866485596}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6265201568603516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6262609958648682},{"id":"https://openalex.org/C172829509","wikidata":"https://www.wikidata.org/wiki/Q4115796","display_name":"Lax pair","level":3,"score":0.5958603024482727},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5698572993278503},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4973318874835968},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4929980933666229},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46540170907974243},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44326454401016235},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3251056969165802},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13331818580627441},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.07618740200996399},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.05662447214126587},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.044696927070617676},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/j.padiff.2024.101014","doi":"https://doi.org/10.1016/j.padiff.2024.101014","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.padiff.2024.101014","pdf_url":null,"source":{"id":"https://openalex.org/S4210214501","display_name":"Partial Differential Equations in Applied Mathematics","issn_l":"2666-8181","issn":["2666-8181"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Partial Differential Equations in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2410.01474","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2410.01474","pdf_url":"https://arxiv.org/pdf/2410.01474","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":"pmh:oai:doaj.org/article:28f23638816246beabe60dab142e5de3","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/28f23638816246beabe60dab142e5de3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Partial Differential Equations in Applied Mathematics, Vol 13, Iss , Pp 101014- (2025)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2410.01474","doi":"https://doi.org/10.48550/arxiv.2410.01474","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2410.01474","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":"article-journal"}],"best_oa_location":{"id":"doi:10.1016/j.padiff.2024.101014","doi":"https://doi.org/10.1016/j.padiff.2024.101014","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.padiff.2024.101014","pdf_url":null,"source":{"id":"https://openalex.org/S4210214501","display_name":"Partial Differential Equations in Applied Mathematics","issn_l":"2666-8181","issn":["2666-8181"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Partial Differential Equations in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1098209393","display_name":null,"funder_award_id":"075-02-2024-1442","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G7733117437","display_name":null,"funder_award_id":"20-71-10110","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"},{"id":"https://openalex.org/G8484229152","display_name":null,"funder_award_id":"075-02-2024-1442","funder_id":"https://openalex.org/F4320321912","funder_display_name":"Ministry of Education and Science of the Russian Federation"}],"funders":[{"id":"https://openalex.org/F4320321912","display_name":"Ministry of Education and Science of the Russian Federation","ror":"https://ror.org/00ghqgy32"},{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"},{"id":"https://openalex.org/F4320327494","display_name":"Ministry of Science and Higher Education of the Russian Federation","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405046151.pdf","grobid_xml":"https://content.openalex.org/works/W4405046151.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1486629500","https://openalex.org/W1965784180","https://openalex.org/W1972309467","https://openalex.org/W1973517317","https://openalex.org/W1977269844","https://openalex.org/W1986514659","https://openalex.org/W2010218678","https://openalex.org/W2022025639","https://openalex.org/W2058893615","https://openalex.org/W2084390415","https://openalex.org/W2084930019","https://openalex.org/W2105117198","https://openalex.org/W2158388352","https://openalex.org/W2198111234","https://openalex.org/W2204264315","https://openalex.org/W2507743553","https://openalex.org/W3105258567","https://openalex.org/W4247298170","https://openalex.org/W4318696274","https://openalex.org/W4400615974","https://openalex.org/W4412027010"],"related_works":["https://openalex.org/W7158576801","https://openalex.org/W4412027010","https://openalex.org/W7155362853","https://openalex.org/W2198111234","https://openalex.org/W4400615974","https://openalex.org/W2544528353","https://openalex.org/W2338475335","https://openalex.org/W7214968672","https://openalex.org/W1997969725","https://openalex.org/W3089759349"],"abstract_inverted_index":{"This":[0],"paper":[1,33],"is":[2],"part":[3,53],"of":[4,19,46,54,59,90,128],"a":[5],"research":[6],"project":[7],"on":[8,64,122],"relations":[9],"between":[10],"differential\u2013difference":[11,30],"matrix":[12],"Lax":[13],"representations":[14],"(MLRs)":[15],"with":[16],"the":[17,35,50,97,119,141,145],"action":[18],"gauge":[20,60],"transformations":[21,25],"and":[22,39,74,113],"discrete":[23,51],"Miura-type":[24],"(MTs)":[26],"for":[27,93],"(nonlinear)":[28],"integrable":[29,76],"equations.":[31,84],"The":[32,101,106],"addresses":[34],"following":[36,98],"problem:":[37],"when":[38],"how":[40],"can":[41],"one":[42],"eliminate":[43],"some":[44],"shifts":[45],"dependent":[47],"variables":[48],"from":[49,134],"(difference)":[52],"an":[55,125],"MLR":[56],"by":[57,79,109,124],"means":[58],"transformations?":[61],"Using":[62],"results":[63,89],"this":[65,91],"problem,":[66],"we":[67,87],"present":[68],"applications":[69],"to":[70,82,96,140],"constructing":[71],"new":[72,75,80],"MLRs":[73],"equations":[77,94],"connected":[78,95],"MTs":[81],"known":[83],"In":[85],"particular,":[86],"obtain":[88],"kind":[92],"ones:":[99],"\u2022":[100,105,131],"two-component":[102],"Belov\u2013Chaltikian":[103],"lattice.":[104],"equation":[107,133],"(introduced":[108],"G.":[110],"Mar\u00ed":[111],"Beffa":[112],"Jing":[114],"Ping":[115],"Wang)":[116],"which":[117],"describes":[118],"evolution":[120,127],"induced":[121],"invariants":[123],"invariant":[126],"planar":[129],"polygons.":[130],"An":[132],"[S.":[135],"Igonin,":[136],"arXiv:2405.08579":[137],"]":[138],"related":[139],"Toda":[142],"lattice":[143],"in":[144],"Flaschka\u2013Manakov":[146],"coordinates.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2024-12-06T00:00:00"}