{"id":"https://openalex.org/W4322774718","doi":"https://doi.org/10.3390/sym15030626","title":"Dynamical Structures of Multi-Solitons and Interaction of Solitons to the Higher-Order KdV-5 Equation","display_name":"Dynamical Structures of Multi-Solitons and Interaction of Solitons to the Higher-Order KdV-5 Equation","publication_year":2023,"publication_date":"2023-03-02","ids":{"openalex":"https://openalex.org/W4322774718","doi":"https://doi.org/10.3390/sym15030626"},"language":"en","primary_location":{"id":"doi:10.3390/sym15030626","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030626","pdf_url":"https://www.mdpi.com/2073-8994/15/3/626/pdf?version=1677746335","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/2073-8994/15/3/626/pdf?version=1677746335","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086562119","display_name":"Fahad Sameer Alshammari","orcid":"https://orcid.org/0000-0002-5402-8960"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Fahad Sameer Alshammari","raw_affiliation_strings":["Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattambin Abdulaziz University, Alkharj 11942, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-5402-8960","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattambin Abdulaziz University, Alkharj 11942, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085703840","display_name":"Zillur Rahman","orcid":"https://orcid.org/0000-0003-2785-0200"},"institutions":[{"id":"https://openalex.org/I288011450","display_name":"Comilla University","ror":"https://ror.org/02bnddg69","country_code":"BD","type":"education","lineage":["https://openalex.org/I288011450"]},{"id":"https://openalex.org/I902853133","display_name":"University of Rajshahi","ror":"https://ror.org/05nnyr510","country_code":"BD","type":"education","lineage":["https://openalex.org/I902853133"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"Zillur Rahman","raw_affiliation_strings":["Department of Mathematics, Comilla University, Cumilla 3506, Bangladesh","Department of Mathematics, Rajshahi University, Rajshahi 6205, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Comilla University, Cumilla 3506, Bangladesh","institution_ids":["https://openalex.org/I288011450"]},{"raw_affiliation_string":"Department of Mathematics, Rajshahi University, Rajshahi 6205, Bangladesh","institution_ids":["https://openalex.org/I902853133"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013417439","display_name":"Harun-Or Roshid","orcid":"https://orcid.org/0000-0002-1687-623X"},"institutions":[{"id":"https://openalex.org/I260446899","display_name":"Pabna University of Science and Technology","ror":"https://ror.org/01vxg3438","country_code":"BD","type":"education","lineage":["https://openalex.org/I260446899"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"Harun-Or Roshid","raw_affiliation_strings":["Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, Bangladesh"],"raw_orcid":"https://orcid.org/0000-0002-1687-623X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, Bangladesh","institution_ids":["https://openalex.org/I260446899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071575512","display_name":"Mohammad Safi Ullah","orcid":"https://orcid.org/0000-0002-8889-7865"},"institutions":[{"id":"https://openalex.org/I288011450","display_name":"Comilla University","ror":"https://ror.org/02bnddg69","country_code":"BD","type":"education","lineage":["https://openalex.org/I288011450"]},{"id":"https://openalex.org/I902853133","display_name":"University of Rajshahi","ror":"https://ror.org/05nnyr510","country_code":"BD","type":"education","lineage":["https://openalex.org/I902853133"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"Mohammad Safi Ullah","raw_affiliation_strings":["Department of Mathematics, Comilla University, Cumilla 3506, Bangladesh","Department of Mathematics, Rajshahi University, Rajshahi 6205, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Comilla University, Cumilla 3506, Bangladesh","institution_ids":["https://openalex.org/I288011450"]},{"raw_affiliation_string":"Department of Mathematics, Rajshahi University, Rajshahi 6205, Bangladesh","institution_ids":["https://openalex.org/I902853133"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089174922","display_name":"Abdullah Aldurayhim","orcid":"https://orcid.org/0000-0003-3174-5323"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Abdullah Aldurayhim","raw_affiliation_strings":["Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattambin Abdulaziz University, Alkharj 11942, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattambin Abdulaziz University, Alkharj 11942, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016544440","display_name":"Md Zulfikar Ali","orcid":"https://orcid.org/0000-0002-7054-0059"},"institutions":[{"id":"https://openalex.org/I902853133","display_name":"University of Rajshahi","ror":"https://ror.org/05nnyr510","country_code":"BD","type":"education","lineage":["https://openalex.org/I902853133"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"M. Zulfikar Ali","raw_affiliation_strings":["Department of Mathematics, Rajshahi University, Rajshahi 6205, Bangladesh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Rajshahi University, Rajshahi 6205, Bangladesh","institution_ids":["https://openalex.org/I902853133"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5086562119"],"corresponding_institution_ids":["https://openalex.org/I142608572"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.891,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.84085476,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"15","issue":"3","first_page":"626","last_page":"626"},"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":0.9993000030517578,"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/T10988","display_name":"Advanced Fiber Laser Technologies","score":0.9503999948501587,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rogue-wave","display_name":"Rogue wave","score":0.8150094747543335},{"id":"https://openalex.org/keywords/breather","display_name":"Breather","score":0.7975026369094849},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.7470932006835938},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6655530333518982},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.6509177088737488},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.5321746468544006},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.527476966381073},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.4420653283596039},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3410447835922241},{"id":"https://openalex.org/keywords/quantum-electrodynamics","display_name":"Quantum electrodynamics","score":0.33715495467185974},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31901946663856506},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2641831636428833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20166578888893127}],"concepts":[{"id":"https://openalex.org/C189201455","wikidata":"https://www.wikidata.org/wiki/Q110360","display_name":"Rogue wave","level":3,"score":0.8150094747543335},{"id":"https://openalex.org/C74455749","wikidata":"https://www.wikidata.org/wiki/Q5254599","display_name":"Breather","level":3,"score":0.7975026369094849},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.7470932006835938},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6655530333518982},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.6509177088737488},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5321746468544006},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.527476966381073},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.4420653283596039},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3410447835922241},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.33715495467185974},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31901946663856506},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2641831636428833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20166578888893127},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15030626","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030626","pdf_url":"https://www.mdpi.com/2073-8994/15/3/626/pdf?version=1677746335","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:aa3e33ba652b46a09cf4c89a3e856fea","is_oa":false,"landing_page_url":"https://doaj.org/article/aa3e33ba652b46a09cf4c89a3e856fea","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 15, Iss 3, p 626 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/3/626/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15030626","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/sym15030626","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030626","pdf_url":"https://www.mdpi.com/2073-8994/15/3/626/pdf?version=1677746335","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":[{"id":"https://openalex.org/F4320311227","display_name":"Prince Sattam bin Abdulaziz University","ror":"https://ror.org/04jt46d36"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4322774718.pdf"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W595846807","https://openalex.org/W1967930895","https://openalex.org/W1989760690","https://openalex.org/W2005674956","https://openalex.org/W2026923035","https://openalex.org/W2030491207","https://openalex.org/W2043756190","https://openalex.org/W2044633502","https://openalex.org/W2104877941","https://openalex.org/W2113843433","https://openalex.org/W2115600080","https://openalex.org/W2128968062","https://openalex.org/W2131477002","https://openalex.org/W2138729229","https://openalex.org/W2199105490","https://openalex.org/W2321660163","https://openalex.org/W2525467566","https://openalex.org/W2901199775","https://openalex.org/W2979819030","https://openalex.org/W3094734074","https://openalex.org/W3102027344","https://openalex.org/W3113073277","https://openalex.org/W3119825491","https://openalex.org/W3126688605","https://openalex.org/W3135110325","https://openalex.org/W3152877862","https://openalex.org/W3188593508","https://openalex.org/W3191773490","https://openalex.org/W3212534417","https://openalex.org/W3215210817","https://openalex.org/W4214939761","https://openalex.org/W4220655824","https://openalex.org/W4281893089","https://openalex.org/W4282945173","https://openalex.org/W4285013053","https://openalex.org/W4285727873","https://openalex.org/W4292310231","https://openalex.org/W4293483810","https://openalex.org/W4296120542","https://openalex.org/W4304099132","https://openalex.org/W4306404469","https://openalex.org/W6727699869","https://openalex.org/W6809665635","https://openalex.org/W6843197863"],"related_works":["https://openalex.org/W4389036002","https://openalex.org/W4398239089","https://openalex.org/W4391329000","https://openalex.org/W3094221240","https://openalex.org/W2884485657","https://openalex.org/W4210419048","https://openalex.org/W2045043406","https://openalex.org/W4388044874","https://openalex.org/W3040477263","https://openalex.org/W4386357002"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"we":[3],"build":[4],"multi-wave":[5],"solutions":[6,26,55],"of":[7,19,30,44,62,78,114,141,154],"the":[8,20,28,42,60,63,70,76,99,132,142,155,159],"KdV-5":[9,72],"model":[10],"through":[11],"Hirota\u2019s":[12],"bilinear":[13],"method.":[14],"Taking":[15],"complex":[16],"conjugate":[17],"values":[18],"free":[21],"parameters,":[22],"various":[23],"colliding":[24,52],"exact":[25],"in":[27,67,83,92,150,158],"form":[29],"rogue":[31,37,48,53],"wave,":[32,49],"symmetric":[33,137],"bell":[34,46],"soliton":[35],"and":[36,47,50,87,89,104,122,127,134],"waves":[38,82],"form;":[39],"breather":[40,64],"waves,":[41,65,115],"interaction":[43],"a":[45,84,116],"two":[51],"wave":[54,143],"are":[56,125,148],"constructed.":[57],"To":[58],"explore":[59],"characteristics":[61],"localized":[66],"any":[68],"direction,":[69],"higher-order":[71],"model,":[73],"which":[74],"describes":[75],"promulgation":[77],"weakly":[79],"nonlinear":[80,156],"elongated":[81],"narrow":[85],"channel,":[86],"ion-acoustic,":[88],"acoustic":[90],"emission":[91],"harmonic":[93],"crystals":[94],"symmetrically":[95],"is":[96],"analyzed.":[97],"With":[98],"appropriate":[100],"parameters":[101],"that":[102],"affect":[103],"manage":[105],"phase":[106],"shifts,":[107],"transmission":[108],"routes,":[109],"as":[110,112],"well":[111],"energies":[113],"mixed":[117],"solution":[118],"relating":[119],"to":[120],"hyperbolic":[121],"sinusoidal":[123],"expression":[124],"derived":[126],"illustrated":[128],"by":[129],"figures.":[130],"All":[131],"single":[133],"multi-soliton":[135],"appeared":[136],"about":[138],"an":[139,152],"axis":[140],"propagation.":[144],"The":[145],"analyzed":[146],"outcomes":[147],"functional":[149],"achieving":[151],"understanding":[153],"situations":[157],"mentioned":[160],"fields.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
