{"id":"https://openalex.org/W4396977024","doi":"https://doi.org/10.3390/axioms13050331","title":"Solving Nonlinear Second-Order ODEs via the Eisenhart Lift and Linearization","display_name":"Solving Nonlinear Second-Order ODEs via the Eisenhart Lift and Linearization","publication_year":2024,"publication_date":"2024-05-16","ids":{"openalex":"https://openalex.org/W4396977024","doi":"https://doi.org/10.3390/axioms13050331"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13050331","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13050331","pdf_url":"https://www.mdpi.com/2075-1680/13/5/331/pdf?version=1715870923","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/5/331/pdf?version=1715870923","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077055758","display_name":"Andronikos Paliathanasis","orcid":"https://orcid.org/0000-0002-9966-5517"},"institutions":[{"id":"https://openalex.org/I177181097","display_name":"Durban University of Technology","ror":"https://ror.org/0303y7a51","country_code":"ZA","type":"education","lineage":["https://openalex.org/I177181097"]},{"id":"https://openalex.org/I2802166871","display_name":"Universidad Cat\u00f3lica del Norte","ror":"https://ror.org/02akpm128","country_code":"CL","type":"education","lineage":["https://openalex.org/I2802166871"]}],"countries":["CL","ZA"],"is_corresponding":true,"raw_author_name":"Andronikos Paliathanasis","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad Cat\u00f3lica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta 1270709, Chile","Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa"],"raw_orcid":"https://orcid.org/0000-0002-9966-5517","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Cat\u00f3lica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta 1270709, Chile","institution_ids":["https://openalex.org/I2802166871"]},{"raw_affiliation_string":"Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa","institution_ids":["https://openalex.org/I177181097"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5077055758"],"corresponding_institution_ids":["https://openalex.org/I177181097","https://openalex.org/I2802166871"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.0196,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70223219,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"13","issue":"5","first_page":"331","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9735999703407288,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9735999703407288,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9715999960899353,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10205","display_name":"Advanced Fiber Optic Sensors","score":0.9544000029563904,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/lift","display_name":"Lift (data mining)","score":0.75855952501297},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5836437344551086},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.5770894885063171},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5749707221984863},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5690403580665588},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5098602175712585},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46262121200561523},{"id":"https://openalex.org/keywords/feedback-linearization","display_name":"Feedback linearization","score":0.438827246427536},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43171146512031555},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3475574254989624},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14855331182479858},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11480385065078735},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.07838785648345947},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.06323924660682678}],"concepts":[{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.75855952501297},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5836437344551086},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.5770894885063171},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5749707221984863},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5690403580665588},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5098602175712585},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46262121200561523},{"id":"https://openalex.org/C85736874","wikidata":"https://www.wikidata.org/wiki/Q672139","display_name":"Feedback linearization","level":3,"score":0.438827246427536},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43171146512031555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3475574254989624},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14855331182479858},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11480385065078735},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.07838785648345947},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.06323924660682678},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13050331","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13050331","pdf_url":"https://www.mdpi.com/2075-1680/13/5/331/pdf?version=1715870923","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:351944a41e5c4f869913874498ecf16f","is_oa":true,"landing_page_url":"https://doaj.org/article/351944a41e5c4f869913874498ecf16f","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,"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":"Axioms, Vol 13, Iss 5, p 331 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13050331","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13050331","pdf_url":"https://www.mdpi.com/2075-1680/13/5/331/pdf?version=1715870923","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4396977024.pdf"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W133191714","https://openalex.org/W1966547119","https://openalex.org/W1967562111","https://openalex.org/W1971348149","https://openalex.org/W1971561274","https://openalex.org/W1972802228","https://openalex.org/W1981141237","https://openalex.org/W1996843793","https://openalex.org/W1997955443","https://openalex.org/W2005699652","https://openalex.org/W2011174098","https://openalex.org/W2023997698","https://openalex.org/W2027355470","https://openalex.org/W2031756342","https://openalex.org/W2034984602","https://openalex.org/W2043550321","https://openalex.org/W2048125573","https://openalex.org/W2048416230","https://openalex.org/W2048981365","https://openalex.org/W2053360550","https://openalex.org/W2054772622","https://openalex.org/W2062294311","https://openalex.org/W2064340569","https://openalex.org/W2064498680","https://openalex.org/W2067628320","https://openalex.org/W2072143191","https://openalex.org/W2080333111","https://openalex.org/W2092649809","https://openalex.org/W2141150708","https://openalex.org/W2145946405","https://openalex.org/W2166052904","https://openalex.org/W2261534158","https://openalex.org/W2312378499","https://openalex.org/W2516807544","https://openalex.org/W2559647002","https://openalex.org/W2797256054","https://openalex.org/W2910558622","https://openalex.org/W2911249005","https://openalex.org/W2913906437","https://openalex.org/W2949475453","https://openalex.org/W2971990086","https://openalex.org/W3022230513","https://openalex.org/W3097996059","https://openalex.org/W3099062590","https://openalex.org/W3117503941","https://openalex.org/W3201957304","https://openalex.org/W3207826324","https://openalex.org/W4292170110","https://openalex.org/W4311998854","https://openalex.org/W4388795629","https://openalex.org/W6759319648"],"related_works":["https://openalex.org/W1998462347","https://openalex.org/W2349527210","https://openalex.org/W4229795303","https://openalex.org/W1836713364","https://openalex.org/W2131265573","https://openalex.org/W2899783744","https://openalex.org/W2964841342","https://openalex.org/W4300511988","https://openalex.org/W130230158","https://openalex.org/W2999135108"],"abstract_inverted_index":{"The":[0,42],"linearization":[1,53],"of":[2,37,47,54,57],"nonlinear":[3],"differential":[4,40],"equations":[5],"represents":[6],"a":[7,22,35,55],"robust":[8],"approach":[9,50],"to":[10],"solution":[11],"derivation,":[12],"typically":[13],"achieved":[14],"through":[15,64],"Lie":[16],"symmetry":[17,65],"analysis.":[18,66],"This":[19],"study":[20],"adopts":[21],"geometric":[23,49],"methodology":[24],"grounded":[25],"in":[26,51],"the":[27,45,52],"Eisenhart":[28],"lift,":[29],"revealing":[30],"transformative":[31],"techniques":[32],"that":[33,60],"linearize":[34],"set":[36],"second-order":[38],"ordinary":[39],"equations.":[41],"research":[43],"underscores":[44],"effectiveness":[46],"this":[48],"class":[56],"Newtonian":[58],"systems":[59],"cannot":[61],"be":[62],"linearized":[63]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}