{"id":"https://openalex.org/W4401964437","doi":"https://doi.org/10.1142/s0217984925500022","title":"Investigating the invariant solutions of (1+1)-dimensional Sawada\u2013Kotera model using Lie symmetries analysis","display_name":"Investigating the invariant solutions of (1+1)-dimensional Sawada\u2013Kotera model using Lie symmetries analysis","publication_year":2024,"publication_date":"2024-08-27","ids":{"openalex":"https://openalex.org/W4401964437","doi":"https://doi.org/10.1142/s0217984925500022"},"language":"en","primary_location":{"id":"doi:10.1142/s0217984925500022","doi":"https://doi.org/10.1142/s0217984925500022","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217984925500022","pdf_url":null,"source":{"id":"https://openalex.org/S88537382","display_name":"Modern Physics Letters B","issn_l":"0217-9849","issn":["0217-9849","1793-6640"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Modern Physics Letters B","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069957230","display_name":"Muhammad Nadeem","orcid":"https://orcid.org/0000-0002-9349-4729","observed_orcids":["https://orcid.org/0000-0002-9349-4729"]},"institutions":[{"id":"https://openalex.org/I4210105365","display_name":"Qujing Normal University","ror":"https://ror.org/02ad7ap24","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210105365"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Muhammad Nadeem","raw_affiliation_strings":["School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, China"],"raw_orcid":"https://orcid.org/0000-0002-9349-4729","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, China","institution_ids":["https://openalex.org/I4210105365"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025898498","display_name":"Shamoona Jabeen","orcid":"https://orcid.org/0000-0002-4367-5708","observed_orcids":["https://orcid.org/0000-0002-4367-5708"]},"institutions":[{"id":"https://openalex.org/I4210154218","display_name":"University of Science and Technology Bannu","ror":"https://ror.org/04be2dn15","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210154218"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Shamoona Jabeen","raw_affiliation_strings":["Department of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-4367-5708","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I4210154218"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081806740","display_name":"Omar Abu Arqub","orcid":"https://orcid.org/0000-0001-9526-6095","observed_orcids":["https://orcid.org/0000-0001-9526-6095"]},"institutions":[{"id":"https://openalex.org/I33926330","display_name":"Al-Balqa Applied University","ror":"https://ror.org/00qedmt22","country_code":"JO","type":"education","lineage":["https://openalex.org/I33926330"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Omar Abu Arqub","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt, 19117, Jordan"],"raw_orcid":"https://orcid.org/0000-0001-9526-6095","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt, 19117, Jordan","institution_ids":["https://openalex.org/I33926330"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7296,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.8354557,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"39","issue":"15","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":0.9990000128746033,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.00019999999494757503,"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"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":9.999999747378752e-05,"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/sawada-kotera-equation","display_name":"Sawada-Kotera equation","score":0.921999990940094},{"id":"https://openalex.org/keywords/1-1-dimensional-nonlinear-evolution-equations","display_name":"(1+1)-dimensional nonlinear evolution equations","score":0.8560000061988831},{"id":"https://openalex.org/keywords/lie-symmetries","display_name":"Lie symmetries","score":0.800000011920929},{"id":"https://openalex.org/keywords/invariant-solutions","display_name":"invariant solutions","score":0.8859999775886536},{"id":"https://openalex.org/keywords/exact-solutions","display_name":"exact solutions","score":0.7250000238418579},{"id":"https://openalex.org/keywords/constant-solutions","display_name":"constant solutions","score":0.7900000214576721},{"id":"https://openalex.org/keywords/planar-dynamical-systems","display_name":"planar dynamical systems","score":0.7710000276565552},{"id":"https://openalex.org/keywords/bifurcation-analysis","display_name":"bifurcation analysis","score":0.9890000224113464},{"id":"https://openalex.org/keywords/sensitivity-analysis","display_name":"sensitivity analysis","score":0.9419999718666077},{"id":"https://openalex.org/keywords/periodic-perturbations","display_name":"periodic perturbations","score":0.847000002861023},{"id":"https://openalex.org/keywords/nonlinear-waves","display_name":"nonlinear waves","score":0.37599998712539673}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6064408421516418},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.590988278388977},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.583307683467865},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5541799664497375},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.49452587962150574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4790938198566437},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46369776129722595},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4565202593803406},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.42894667387008667},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3544577360153198},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3373107612133026},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.303419291973114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28400278091430664},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19186893105506897},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.16648036241531372},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0965244472026825},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09181329607963562},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07671099901199341}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0217984925500022","doi":"https://doi.org/10.1142/s0217984925500022","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217984925500022","pdf_url":null,"source":{"id":"https://openalex.org/S88537382","display_name":"Modern Physics Letters B","issn_l":"0217-9849","issn":["0217-9849","1793-6640"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Modern Physics Letters B","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W2321307647","https://openalex.org/W2781681256","https://openalex.org/W2915027708","https://openalex.org/W2922327616","https://openalex.org/W3106489632","https://openalex.org/W3129107470","https://openalex.org/W3138137334","https://openalex.org/W3175740033","https://openalex.org/W3214990695","https://openalex.org/W4285611399","https://openalex.org/W4292260715","https://openalex.org/W4294874565","https://openalex.org/W4296445336","https://openalex.org/W4309726408","https://openalex.org/W4311985775","https://openalex.org/W4312056925","https://openalex.org/W4313650666","https://openalex.org/W4317623163","https://openalex.org/W4323356987","https://openalex.org/W4360850983","https://openalex.org/W4362513967","https://openalex.org/W4372284531","https://openalex.org/W4375846088","https://openalex.org/W4380878585","https://openalex.org/W4381662066","https://openalex.org/W4382645087","https://openalex.org/W4385069986","https://openalex.org/W4388141307","https://openalex.org/W4389795403","https://openalex.org/W4390414672","https://openalex.org/W4390517505","https://openalex.org/W4390703472","https://openalex.org/W4390750550","https://openalex.org/W4391537935","https://openalex.org/W4394064247"],"related_works":["https://openalex.org/W2574164518","https://openalex.org/W4300511534","https://openalex.org/W2964376029","https://openalex.org/W2259916391","https://openalex.org/W4391503114","https://openalex.org/W3144866039","https://openalex.org/W2795382500","https://openalex.org/W2507817553","https://openalex.org/W3008944339","https://openalex.org/W2991139164"],"abstract_inverted_index":{"Here":[0],"attention":[1],"is":[2,11,48,121,177],"focused":[3],"on":[4,31],"the":[5,32,41,45,56,61,77,89,102,109,115,134,158,168,174,199,205,218],"(1+1)-dimensional":[6],"Sawada\u2013Kotera":[7],"(SK)":[8],"model":[9,47,176],"that":[10,83,153],"prominent":[12],"in":[13,88,157],"mathematical":[14],"physics":[15],"and":[16,21,35,59,69,98,129,194,204,209],"engineering":[17],"to":[18,50,67,166,179],"analyze":[19],"plasmas":[20],"coherent":[22],"systems":[23],"for":[24,197],"communication.":[25],"Our":[26],"techniques":[27],"offer":[28,93],"fresh":[29],"perspectives":[30,125],"model\u2019s":[33],"attributes":[34],"structure,":[36],"deepening":[37],"our":[38],"comprehension":[39],"of":[40,79,96,108,118,137,173,221],"underlying":[42],"dynamics.":[43],"First,":[44],"SK":[46,103,175],"reduced":[49],"ordinary":[51],"differential":[52],"equations":[53],"by":[54,105,141,217],"constructing":[55],"Lie":[57,110],"symmetries":[58,111],"using":[60,142],"associated":[62],"transformation.":[63],"Graphs":[64],"are":[65,164,191,214],"used":[66],"build":[68],"display":[70,167],"invariant":[71,169],"solutions.":[72,170],"This":[73],"strategy":[74],"has":[75],"caused":[76],"revelation":[78],"novel":[80],"constant":[81],"solutions":[82],"have":[84],"not":[85],"been":[86],"found":[87],"previous":[90],"works.":[91],"We":[92,132,145],"new":[94,212],"understandings":[95],"nature":[97],"changes":[99],"observed":[100],"during":[101],"derivation":[104],"taking":[106],"advantage":[107],"powerful":[112],"tools.":[113],"Next,":[114],"fluctuating":[116],"layout":[117],"proposed":[119],"framework":[120],"examined":[122,133],"from":[123],"several":[124],"such":[126],"as":[127],"sensitivity":[128,172,183],"bifurcation":[130,135,143],"analysis.":[131],"analysis":[136,184],"planar":[138],"dynamical":[139,160],"system":[140,222],"theory.":[144],"also":[146],"include":[147],"an":[148],"external":[149],"periodic":[150],"perturbation":[151],"term":[152],"breaks":[154],"regular":[155],"patterns":[156],"perturbed":[159],"system.":[161],"Graphical":[162],"structures":[163],"provided":[165],"The":[171],"determined":[178],"be":[180],"strong":[181],"after":[182],"under":[185],"different":[186],"initial":[187],"conditions.":[188],"These":[189],"results":[190],"fascinating,":[192],"fresh,":[193],"conceptually":[195],"useful":[196],"understanding":[198],"suggested":[200],"framework.":[201],"In":[202],"mathematics":[203],"applied":[206],"sciences,":[207],"forecasting":[208],"learning":[210],"about":[211],"technologies":[213],"greatly":[215],"aided":[216],"dynamic":[219],"aspect":[220],"processing.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":8}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2024-08-29T00:00:00"}
