{"id":"https://openalex.org/W4409143895","doi":"https://doi.org/10.3390/sym17040546","title":"Symmetries and Closed-Form Solutions for Some Classes of Dynamical Systems","display_name":"Symmetries and Closed-Form Solutions for Some Classes of Dynamical Systems","publication_year":2025,"publication_date":"2025-04-03","ids":{"openalex":"https://openalex.org/W4409143895","doi":"https://doi.org/10.3390/sym17040546"},"language":"en","primary_location":{"id":"doi:10.3390/sym17040546","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040546","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/sym17040546","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060098200","display_name":"Remus-Daniel Ene","orcid":"https://orcid.org/0000-0002-1679-1498"},"institutions":[{"id":"https://openalex.org/I3122695212","display_name":"Polytechnic University of Timi\u015foara","ror":"https://ror.org/02v91gy68","country_code":"RO","type":"education","lineage":["https://openalex.org/I3122695212"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Remus-Daniel Ene","raw_affiliation_strings":["Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania","institution_ids":["https://openalex.org/I3122695212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019364016","display_name":"Nicolina Pop","orcid":"https://orcid.org/0000-0002-7051-6753"},"institutions":[{"id":"https://openalex.org/I3122695212","display_name":"Polytechnic University of Timi\u015foara","ror":"https://ror.org/02v91gy68","country_code":"RO","type":"education","lineage":["https://openalex.org/I3122695212"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Nicolina Pop","raw_affiliation_strings":["Department of Physical Foundations of Engineering, Politehnica University of Timisoara, 2 Vasile Parvan Blvd., 300223 Timisoara, Romania"],"affiliations":[{"raw_affiliation_string":"Department of Physical Foundations of Engineering, Politehnica University of Timisoara, 2 Vasile Parvan Blvd., 300223 Timisoara, Romania","institution_ids":["https://openalex.org/I3122695212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009909766","display_name":"Rodica B\u0103d\u0103r\u0103u","orcid":null},"institutions":[{"id":"https://openalex.org/I3122695212","display_name":"Polytechnic University of Timi\u015foara","ror":"https://ror.org/02v91gy68","country_code":"RO","type":"education","lineage":["https://openalex.org/I3122695212"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Rodica Badarau","raw_affiliation_strings":["Department of Mechanical Machines, Equipment and Transportation, Politehnica University of Timisoara, 1 Mihai Viteazul Blvd., 300222 Timisoara, Romania"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Machines, Equipment and Transportation, Politehnica University of Timisoara, 1 Mihai Viteazul Blvd., 300222 Timisoara, Romania","institution_ids":["https://openalex.org/I3122695212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060098200"],"corresponding_institution_ids":["https://openalex.org/I3122695212"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.4222,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.80550084,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"4","first_page":"546","last_page":"546"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9977999925613403,"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":0.9977999925613403,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9977999925613403,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.7580370903015137},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5919201970100403},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46082815527915955},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4426797926425934},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42225033044815063},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3330111801624298},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28505855798721313},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11500570178031921},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.06949296593666077},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06762823462486267}],"concepts":[{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.7580370903015137},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5919201970100403},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46082815527915955},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4426797926425934},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42225033044815063},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3330111801624298},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28505855798721313},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11500570178031921},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.06949296593666077},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06762823462486267},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17040546","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040546","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17040546","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040546","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1969004631","https://openalex.org/W1982362811","https://openalex.org/W1986806824","https://openalex.org/W1995353980","https://openalex.org/W1999439347","https://openalex.org/W2002684931","https://openalex.org/W2025706341","https://openalex.org/W2030141671","https://openalex.org/W2036356861","https://openalex.org/W2145069124","https://openalex.org/W2522822766","https://openalex.org/W2607115034","https://openalex.org/W2746669530","https://openalex.org/W2891280105","https://openalex.org/W2916366125","https://openalex.org/W2962693352","https://openalex.org/W3134019536","https://openalex.org/W4229672964","https://openalex.org/W4298144482","https://openalex.org/W4300961846","https://openalex.org/W4387985659","https://openalex.org/W4391177983","https://openalex.org/W4391735105","https://openalex.org/W4395003184","https://openalex.org/W4404722740"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W4298192601","https://openalex.org/W1594396050"],"abstract_inverted_index":{"The":[0,37,70,89,138],"present":[1],"paper":[2],"focuses":[3],"on":[4,19,94],"some":[5],"classes":[6],"of":[7,39,43,91,103,120,130,140,146],"dynamical":[8,71,147],"systems":[9,148],"involving":[10],"Hamilton\u2013Poisson":[11],"structures,":[12],"while":[13],"neglecting":[14],"their":[15],"chaotic":[16],"behaviors.":[17],"Based":[18],"this,":[20],"the":[21,31,40,44,52,86,95,101,109,118,121,128,131,135,144],"closed-form":[22],"solutions":[23,27],"are":[24,28,55,58,65],"obtained.":[25],"These":[26],"derived":[29],"using":[30],"Optimal":[32],"Auxiliary":[33],"Functions":[34],"Method":[35],"(OAFM).":[36],"impact":[38],"physical":[41,156],"parameters":[42],"system":[45,72,96],"is":[46,73,82,97,115],"also":[47],"investigated.":[48],"Periodic":[49],"orbits":[50,62],"around":[51],"equilibrium":[53],"points":[54],"performed.":[56],"There":[57],"homoclinic":[59],"or":[60],"heteroclinic":[61],"and":[63,111,152,157],"they":[64],"obtained":[66],"in":[67],"exact":[68],"form.":[69],"reduced":[74],"to":[75],"a":[76],"second-order":[77],"nonlinear":[78],"differential":[79],"equation,":[80],"which":[81],"analytically":[83],"solved":[84],"through":[85],"OAFM":[87,132],"procedure.":[88],"influence":[90],"initial":[92],"conditions":[93],"explored,":[98],"specifically":[99],"regarding":[100],"presence":[102],"symmetries.":[104],"A":[105,124],"good":[106],"agreement":[107],"between":[108],"analytical":[110],"corresponding":[112],"numerical":[113],"results":[114,139],"demonstrated,":[116],"reflecting":[117],"accuracy":[119],"proposed":[122],"method.":[123,137],"comparative":[125],"analysis":[126],"underlines":[127],"advantages":[129],"compared":[133],"with":[134,149],"iterative":[136],"this":[141],"work":[142],"encourage":[143],"study":[145],"bi-Hamiltonian":[150],"structure":[151],"similar":[153],"properties":[154],"as":[155],"biological":[158],"problems.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}