{"id":"https://openalex.org/W4294958819","doi":"https://doi.org/10.3390/sym14091861","title":"Conservation Laws and Travelling Wave Solutions for a Negative-Order KdV-CBS Equation in 3+1 Dimensions","display_name":"Conservation Laws and Travelling Wave Solutions for a Negative-Order KdV-CBS Equation in 3+1 Dimensions","publication_year":2022,"publication_date":"2022-09-06","ids":{"openalex":"https://openalex.org/W4294958819","doi":"https://doi.org/10.3390/sym14091861"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091861","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091861","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1861/pdf?version=1663750821","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","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/9/1861/pdf?version=1663750821","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040735583","display_name":"M.L. Gandarias","orcid":"https://orcid.org/0000-0001-8604-8272"},"institutions":[{"id":"https://openalex.org/I39147953","display_name":"Universidad de C\u00e1diz","ror":"https://ror.org/04mxxkb11","country_code":"ES","type":"education","lineage":["https://openalex.org/I39147953"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Maria Luz Gandarias","raw_affiliation_strings":["Department of Mathematics, University of Cadiz, 11510 Puerto Real, Spain"],"raw_orcid":"https://orcid.org/0000-0001-8604-8272","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Cadiz, 11510 Puerto Real, Spain","institution_ids":["https://openalex.org/I39147953"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071287576","display_name":"Nauman Raza","orcid":"https://orcid.org/0000-0003-0700-1033"},"institutions":[{"id":"https://openalex.org/I172780181","display_name":"University of the Punjab","ror":"https://ror.org/011maz450","country_code":"PK","type":"education","lineage":["https://openalex.org/I172780181"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Nauman Raza","raw_affiliation_strings":["Department of Mathematics, Quaid-e-Azam Campus, University of the Punjab, Lahore 54000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-e-Azam Campus, University of the Punjab, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I172780181"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040735583"],"corresponding_institution_ids":["https://openalex.org/I39147953"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.2345,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.78306189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"9","first_page":"1861","last_page":"1861"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"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":1.0,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9943000078201294,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9682999849319458,"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/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.8981809616088867},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.8469630479812622},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.677210807800293},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6547983884811401},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6083166599273682},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5876649022102356},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.5650960206985474},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.5536205172538757},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5249171853065491},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.5149906277656555},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.46596696972846985},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45995935797691345},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34038132429122925},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3276407718658447},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19982731342315674},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07130727171897888}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.8981809616088867},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8469630479812622},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.677210807800293},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6547983884811401},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6083166599273682},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5876649022102356},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.5650960206985474},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5536205172538757},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5249171853065491},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.5149906277656555},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.46596696972846985},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45995935797691345},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34038132429122925},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3276407718658447},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19982731342315674},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07130727171897888},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym14091861","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091861","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1861/pdf?version=1663750821","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"},{"id":"pmh:oai:rodin.uca.es:10498/28380","is_oa":true,"landing_page_url":"http://hdl.handle.net/10498/28380","pdf_url":"https://rodin.uca.es/bitstream/10498/28380/1/2022_672.pdf","source":{"id":"https://openalex.org/S4306400506","display_name":"RODIN (Universidad de C\u00e1diz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39147953","host_organization_name":"Universidad de C\u00e1diz","host_organization_lineage":["https://openalex.org/I39147953"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol. 14, N\u00fam. 9, 2022","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:7e512b7d16b34f64b0290b2fd4349910","is_oa":true,"landing_page_url":"https://doaj.org/article/7e512b7d16b34f64b0290b2fd4349910","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":"Symmetry, Vol 14, Iss 9, p 1861 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1861/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091861","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14091861","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091861","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1861/pdf?version=1663750821","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":[{"display_name":"Life in Land","score":0.6899999976158142,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4294958819.pdf","grobid_xml":"https://content.openalex.org/works/W4294958819.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1506397612","https://openalex.org/W1983393596","https://openalex.org/W2005161810","https://openalex.org/W2010543169","https://openalex.org/W2018661297","https://openalex.org/W2046099083","https://openalex.org/W2048133902","https://openalex.org/W2051959080","https://openalex.org/W2052199721","https://openalex.org/W2063864918","https://openalex.org/W2072009618","https://openalex.org/W2082921691","https://openalex.org/W2085493421","https://openalex.org/W2090186503","https://openalex.org/W2165858396","https://openalex.org/W2404293814","https://openalex.org/W2507817553","https://openalex.org/W2606848891","https://openalex.org/W2611830051","https://openalex.org/W2619753037","https://openalex.org/W2748277091","https://openalex.org/W2796560985","https://openalex.org/W2802538198","https://openalex.org/W2807399202","https://openalex.org/W2885044211","https://openalex.org/W2890918665","https://openalex.org/W2901708090","https://openalex.org/W2908123555","https://openalex.org/W3006051830","https://openalex.org/W3034915735","https://openalex.org/W3035924318","https://openalex.org/W3080841052","https://openalex.org/W3096305049","https://openalex.org/W3129756690","https://openalex.org/W3163506188","https://openalex.org/W4224989408","https://openalex.org/W4229672964","https://openalex.org/W4252904065","https://openalex.org/W4283513479","https://openalex.org/W4292170110","https://openalex.org/W6663612268","https://openalex.org/W6666524748","https://openalex.org/W6725114010","https://openalex.org/W6743326281","https://openalex.org/W6745869886"],"related_works":["https://openalex.org/W1985080983","https://openalex.org/W2102153656","https://openalex.org/W2774129652","https://openalex.org/W2056035810","https://openalex.org/W2263050974","https://openalex.org/W2223488821","https://openalex.org/W2353815637","https://openalex.org/W2067598262","https://openalex.org/W2016664673","https://openalex.org/W1971248990"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,28],"study":[4],"a":[5,15,53,57,116],"new":[6],"negative-order":[7],"KdV-CBS":[8],"equation":[9,22,36,62,83],"in":[10,111,115],"(3+1)":[11],"dimensions":[12],"which":[13,64],"is":[14],"combination":[16],"of":[17,34,81,118],"the":[18,30,35,42,78],"Korteweg-de":[19],"Vries":[20],"(KdV)":[21],"and":[23,37,70,85],"Calogero\u2013Bogoyavlenskii\u2013Schiff":[24],"(CBS)":[25],"equation.":[26],"Firstly,":[27],"determine":[29],"Lie":[31],"point":[32],"symmetries":[33],"conservation":[38,46],"laws":[39,47],"by":[40],"using":[41],"multiplier":[43],"method.":[44],"The":[45],"will":[48],"be":[49,108],"used":[50],"to":[51,56,66,95,99],"obtain":[52],"triple":[54],"reduction":[55],"second":[58],"order":[59],"ordinary":[60],"differential":[61],"(ODE),":[63],"lead":[65],"line":[67],"travelling":[68],"waves":[69],"soliton":[71],"solutions.":[72],"Such":[73],"solitons":[74],"are":[75,86],"obtained":[76],"via":[77],"modified":[79],"form":[80],"simple":[82],"method":[84],"displayed":[87],"through":[88],"three-dimensional":[89],"plots":[90],"at":[91],"specific":[92],"parameter":[93],"values":[94],"lend":[96],"physical":[97,113],"meaning":[98],"nonlinear":[100],"phenomena.":[101],"It":[102],"illustrates":[103],"that":[104],"these":[105],"solutions":[106],"might":[107],"extremely":[109],"beneficial":[110],"understanding":[112],"phenomena":[114],"variety":[117],"applied":[119],"mathematics":[120],"areas.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-12T07:12:00.856984","created_date":"2025-10-10T00:00:00"}
