Dynamical behavior of the fractional coupled Konopelchenko-Dubrovsky and (3+1)-dimensional modified Korteweg-de Veries- Zakharov- Kuznestsov equations

Dynamical behavior of the fractional coupled Konopelchenko-Dubrovsky and (3+1)-dimensional modified Korteweg-de Veries- Zakharov- Kuznestsov equations | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Dynamical behavior of the fractional coupled Konopelchenko-Dubrovsky and (3+1)-dimensional modified Korteweg-de Veries- Zakharov- Kuznestsov equations Arslan Aslam, Abdul Majeed, Mohsin Kamran, Mustafa Inc This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2231698/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Apr, 2023 Read the published version in Optical and Quantum Electronics → Version 1 posted 8 You are reading this latest preprint version Abstract This work studies, soliton solutions of time fractional coupled Konopelchenko-Dubrovsky and (3+1)-dimensional modified Korteweg-de Varies-Zakharov-Kuznestsov (mKdVZK) equations. These model are used to define the physical phenomena of oceans dynamic, plasma physics, and soliton theory. The unified method is used to solve these fractional models analytically. Conformable and Local M derivatives are used to tackle the time fractional part. Fractional wave transformation is used to transforme fractional partial differential equation to ordinary differential equation. Using proposed scheme soliton solutions are obtained in polynomial and rational forms. The behaviour of soliton solution is also analyzed at different fractional parameter. The results shows that proposed scheme is straight forward and easy to handle all kinds of time fractional nonlinear homogenous evolution equations that arised in different fields of science. Konopelchenko-Dubrovsky equation modified Korteweg-de Vries-Zakharov-Kuznestsov equation Fractional order Conformable derivative (FCD) LocalM derivative (LMD) analytical solutions Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Apr, 2023 Read the published version in Optical and Quantum Electronics → Version 1 posted Editorial decision: Major revision 03 Dec, 2022 Reviews received at journal 04 Nov, 2022 Reviewers agreed at journal 04 Nov, 2022 Reviewers agreed at journal 04 Nov, 2022 Reviewers invited by journal 04 Nov, 2022 Editor assigned by journal 03 Nov, 2022 Submission checks completed at journal 03 Nov, 2022 First submitted to journal 02 Nov, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2231698","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":149197595,"identity":"af2f48f1-1702-4254-8b35-70ef7217feaa","order_by":0,"name":"Arslan Aslam","email":"","orcid":"","institution":"University of Education Lahore","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Arslan","middleName":"","lastName":"Aslam","suffix":""},{"id":149197596,"identity":"733f0c2b-e181-4c17-8663-4cb396f86164","order_by":1,"name":"Abdul Majeed","email":"","orcid":"","institution":"University of Education Lahore","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Abdul","middleName":"","lastName":"Majeed","suffix":""},{"id":149197597,"identity":"5ad76c90-ca9e-4588-848c-a752bd9e11b0","order_by":2,"name":"Mohsin Kamran","email":"","orcid":"","institution":"University of Education Lahore","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Mohsin","middleName":"","lastName":"Kamran","suffix":""},{"id":149197598,"identity":"4cd18a37-c744-47d9-9268-071a633c6b8d","order_by":3,"name":"Mustafa Inc","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuUlEQVRIiWNgGAWjYDACZiD+YCMB4fAQq4VxRhpQCxtEiwRxunjSGEjQotvOe/CzTYJFPv/8BsYHb9sY6swbCGgxO8yXLJ2TIGE54xgDs+HcNgYJmQMEtfCYMef+kDBgOMbAJs0L1ELQZWAtFgkSBvLHGNh/E6+FAajFAGgLM7FajCV7gFoMjyU2S845JyE5g6CW82cMP/xIqDOQO3z44Ic3ZTb8xEUMBDA2MBAbk6NgFIyCUTAKCAAASNcwTe/7HmAAAAAASUVORK5CYII=","orcid":"","institution":"Firat University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Mustafa","middleName":"","lastName":"Inc","suffix":""}],"badges":[],"createdAt":"2022-11-02 20:59:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2231698/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2231698/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11082-023-04704-0","type":"published","date":"2023-04-21T20:32:42+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":44726950,"identity":"e52b8956-1c1c-4a7f-baa0-ffd5d4f84490","added_by":"auto","created_at":"2023-10-16 20:50:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":378168,"visible":true,"origin":"","legend":"","description":"","filename":"cleanfile.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2231698/v1_covered_e6496111-e33b-4577-8f47-fdcb38e402f4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamical behavior of the fractional coupled Konopelchenko-Dubrovsky and (3+1)-dimensional modified Korteweg-de Veries- Zakharov- Kuznestsov equations","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"optical-and-quantum-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"oqel","sideBox":"Learn more about [Optical and Quantum Electronics](https://www.springer.com/journal/11082)","snPcode":"11082","submissionUrl":"https://submission.nature.com/new-submission/11082/3","title":"Optical and Quantum Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Konopelchenko-Dubrovsky equation, modified Korteweg-de Vries-Zakharov-Kuznestsov equation, Fractional order Conformable derivative (FCD), LocalM derivative (LMD), analytical solutions","lastPublishedDoi":"10.21203/rs.3.rs-2231698/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2231698/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This work studies, soliton solutions of time fractional coupled Konopelchenko-Dubrovsky and (3+1)-dimensional modified Korteweg-de Varies-Zakharov-Kuznestsov (mKdVZK) equations. 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