{"id":"https://openalex.org/W4406334830","doi":"https://doi.org/10.3390/sym17010102","title":"Solutions of Cauchy Problems for the Gardner Equation in Three Spatial Dimensions","display_name":"Solutions of Cauchy Problems for the Gardner Equation in Three Spatial Dimensions","publication_year":2025,"publication_date":"2025-01-11","ids":{"openalex":"https://openalex.org/W4406334830","doi":"https://doi.org/10.3390/sym17010102"},"language":"en","primary_location":{"id":"doi:10.3390/sym17010102","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010102","pdf_url":"https://www.mdpi.com/2073-8994/17/1/102/pdf?version=1736844491","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/2073-8994/17/1/102/pdf?version=1736844491","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023483762","display_name":"Yufeng Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]},{"id":"https://openalex.org/I4210139779","display_name":"Yantai Nanshan University","ror":"https://ror.org/0499b1896","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210139779"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yufeng Zhang","raw_affiliation_strings":["College of Technology and Data, Yantai Nanshan University, Yantai 265713, China","School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Technology and Data, Yantai Nanshan University, Yantai 265713, China","institution_ids":["https://openalex.org/I4210139779"]},{"raw_affiliation_string":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100617866","display_name":"Linlin Gui","orcid":"https://orcid.org/0000-0003-1170-9085"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Linlin Gui","raw_affiliation_strings":["School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111693943","display_name":"Binlu Feng","orcid":null},"institutions":[{"id":"https://openalex.org/I4210139779","display_name":"Yantai Nanshan University","ror":"https://ror.org/0499b1896","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210139779"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Binlu Feng","raw_affiliation_strings":["College of Technology and Data, Yantai Nanshan University, Yantai 265713, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Technology and Data, Yantai Nanshan University, Yantai 265713, China","institution_ids":["https://openalex.org/I4210139779"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100617866"],"corresponding_institution_ids":["https://openalex.org/I25757504"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.6642,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.95218824,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"17","issue":"1","first_page":"102","last_page":"102"},"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":0.9973000288009644,"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":0.9969000220298767,"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/formalism","display_name":"Formalism (music)","score":0.6795746088027954},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.6503362655639648},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.6278578639030457},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6254423260688782},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.5425345301628113},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37826842069625854},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3628796935081482}],"concepts":[{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.6795746088027954},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.6503362655639648},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.6278578639030457},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6254423260688782},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.5425345301628113},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37826842069625854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3628796935081482},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym17010102","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010102","pdf_url":"https://www.mdpi.com/2073-8994/17/1/102/pdf?version=1736844491","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:doaj.org/article:7a3f1de4d8c44b0d9277761a0e392584","is_oa":false,"landing_page_url":"https://doaj.org/article/7a3f1de4d8c44b0d9277761a0e392584","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 17, Iss 1, p 102 (2025)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/17/1/102/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym17010102","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/sym17010102","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010102","pdf_url":"https://www.mdpi.com/2073-8994/17/1/102/pdf?version=1736844491","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":[{"id":"https://openalex.org/G2742536146","display_name":null,"funder_award_id":"No.12371256","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4536593145","display_name":null,"funder_award_id":"11971475","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6647390541","display_name":null,"funder_award_id":"12371256","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6678499769","display_name":null,"funder_award_id":"No.11971475","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4406334830.pdf"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1631607997","https://openalex.org/W1964355484","https://openalex.org/W1982401048","https://openalex.org/W1982554459","https://openalex.org/W1986197169","https://openalex.org/W1994309388","https://openalex.org/W1994528349","https://openalex.org/W2001983765","https://openalex.org/W2003336923","https://openalex.org/W2003409322","https://openalex.org/W2004706791","https://openalex.org/W2004959051","https://openalex.org/W2011429043","https://openalex.org/W2013985944","https://openalex.org/W2014342823","https://openalex.org/W2030669316","https://openalex.org/W2040321162","https://openalex.org/W2043804121","https://openalex.org/W2055354429","https://openalex.org/W2055545390","https://openalex.org/W2061206360","https://openalex.org/W2061301691","https://openalex.org/W2066834343","https://openalex.org/W2075965386","https://openalex.org/W2083960709","https://openalex.org/W2161475106","https://openalex.org/W2467299677","https://openalex.org/W2807912837","https://openalex.org/W2891748839","https://openalex.org/W2962862050","https://openalex.org/W3028302063","https://openalex.org/W3102883330","https://openalex.org/W3128465440","https://openalex.org/W3174930944","https://openalex.org/W3189523937","https://openalex.org/W4288046963","https://openalex.org/W4392612187","https://openalex.org/W4405847635","https://openalex.org/W6752055262"],"related_works":["https://openalex.org/W2078366360","https://openalex.org/W2400581667","https://openalex.org/W2049761058","https://openalex.org/W4213342640","https://openalex.org/W2394174381","https://openalex.org/W4394654496","https://openalex.org/W2020390959","https://openalex.org/W2892071505","https://openalex.org/W2345019225","https://openalex.org/W1968696210"],"abstract_inverted_index":{"In":[0],"this":[1,87],"paper,":[2],"we":[3],"generalize":[4],"the":[5,27,30,37,63,68,83],"2":[6,23],"+":[7,18,22],"1-dimensional":[8],"Gardner":[9,38,69],"(2DG)":[10],"equation":[11,39,70],"to":[12,61],"three":[13,41,72],"spatial":[14,42,73],"dimensions,":[15,24],"i.e.,":[16],"3":[17,21,81],"1":[19,79],"and":[20,25,33,57,80],"construct":[26],"solutions":[28],"of":[29,86],"Cauchy":[31],"problems":[32,66],"Lax":[34],"pairs":[35],"for":[36,67],"in":[40,71],"dimensions":[43],"via":[44],"a":[45],"novel":[46],"non-local":[47],"d-bar":[48],"formalism.":[49],"Several":[50],"new":[51],"long":[52],"derivative":[53],"operators":[54],"Dx,":[55],"Dy":[56],"Dt":[58],"are":[59],"introduced":[60],"study":[62],"initial":[64],"value":[65],"dimensions.":[74],"It":[75],"follows":[76],"that":[77],"Propositions":[78],"summarize":[82],"main":[84],"results":[85],"paper.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}