Dynamical behaviors of vector localized wave solutions for the coupled modified Korteweg-de Vries equations

Dynamical behaviors of vector localized wave solutions for the coupled modified Korteweg-de Vries 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 behaviors of vector localized wave solutions for the coupled modified Korteweg-de Vries equations Yi-Xin Chen, YuFeng Wang, ShengXiong Yang, Xi Zhang, YiTian Gao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4671270/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Aug, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted 17 You are reading this latest preprint version Abstract Under investigation in this paper is the coupled modified Korteweg-de Vries equations. Based on Lax pair and Darboux transformation, various vector localized wave solutions are derived and analyzed. We notice that the localized waves have different dynamical behaviors in several components, for example, the bell-shaped soliton and flat-top soliton, or the bell-shaped soliton and two-peak soli-ton, are obtained in two components, respectively. Furthermore, the interactions between two solitons are different in distinct components. In addition, the vector breather and rogue wave solutions are constructed. Especially, the various structures of first-order rogue waves are observed, such as the two-peak rogue waves and flat-top rogue wave, or the dark rogue waves and bright rogue waves. Finally , the vector second-order rogue wave solutions are derived and the strong or weak interaction patterns of second-order rogue waves are achieved. Coupled modified Korteweg-de Vries equations Vector localized wave Dynamical behav- ior Darboux transformation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Aug, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 09 Jul, 2024 Reviewers agreed at journal 09 Jul, 2024 Reviews received at journal 09 Jul, 2024 Reviews received at journal 09 Jul, 2024 Reviewers agreed at journal 09 Jul, 2024 Reviews received at journal 09 Jul, 2024 Reviewers agreed at journal 06 Jul, 2024 Reviewers agreed at journal 06 Jul, 2024 Reviewers agreed at journal 06 Jul, 2024 Reviewers agreed at journal 06 Jul, 2024 Reviewers agreed at journal 06 Jul, 2024 Reviewers agreed at journal 06 Jul, 2024 Reviewers agreed at journal 06 Jul, 2024 Reviewers invited by journal 06 Jul, 2024 Editor assigned by journal 06 Jul, 2024 Submission checks completed at journal 03 Jul, 2024 First submitted to journal 02 Jul, 2024 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-4671270","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":324697834,"identity":"145cb844-88ea-43ea-9690-0e04c88a37ba","order_by":0,"name":"Yi-Xin Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIie3RMWvCQBTA8RcevC6vyfoKolvnc8kkfpYcgZsUHDM4CIoObelqv4WjY8NBXK67Y8QvoJuDiDq3JHHrcL/5/rx7dwCe9w9RZ785HFj6hJiXSTauT0IwJli2emn0RKkqXVGftGEQI/dM8PXJry+7GTa4GBSm5IFFZZkyPSGIFm9JdRJMN0qcDZV9LrZ63QJxP6vqBCmR7vt9Smi22hEoGdYkxEr0xQYry/FIz7FBwhzLN9/Wn3IMzRKhtDvh2yMjpZK4gmt36Swx35/vXxnZ/HjKxu1o8VGd/MKPHfc8z/P+dAVG20V2gKISGwAAAABJRU5ErkJggg==","orcid":"","institution":"Minzu University of China","correspondingAuthor":true,"prefix":"","firstName":"Yi-Xin","middleName":"","lastName":"Chen","suffix":""},{"id":324697835,"identity":"b7151981-2de6-4196-b2af-a3a1bbe2df44","order_by":1,"name":"YuFeng Wang","email":"","orcid":"","institution":"Minzu University of China","correspondingAuthor":false,"prefix":"","firstName":"YuFeng","middleName":"","lastName":"Wang","suffix":""},{"id":324697836,"identity":"38686eb8-2f3e-4f57-acde-47e3f9ad1d1a","order_by":2,"name":"ShengXiong Yang","email":"","orcid":"","institution":"Minzu University of China","correspondingAuthor":false,"prefix":"","firstName":"ShengXiong","middleName":"","lastName":"Yang","suffix":""},{"id":324697837,"identity":"505835bb-4cda-4d0c-83ca-1daaa65d3afd","order_by":3,"name":"Xi Zhang","email":"","orcid":"","institution":"Minzu University of China","correspondingAuthor":false,"prefix":"","firstName":"Xi","middleName":"","lastName":"Zhang","suffix":""},{"id":324697838,"identity":"5a5f73b2-51c4-4be2-976c-e8aaf2a12840","order_by":4,"name":"YiTian Gao","email":"","orcid":"","institution":"Minzu University of China","correspondingAuthor":false,"prefix":"","firstName":"YiTian","middleName":"","lastName":"Gao","suffix":""}],"badges":[],"createdAt":"2024-07-02 04:06:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4671270/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4671270/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-024-10051-w","type":"published","date":"2024-08-05T15:58:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":62298562,"identity":"040ff329-f127-49aa-9918-7515b808fb1c","added_by":"auto","created_at":"2024-08-12 16:14:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6164844,"visible":true,"origin":"","legend":"","description":"","filename":"cmKdV.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4671270/v1_covered_06324541-d576-4192-86db-57d94fa22b96.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dynamical behaviors of vector localized wave solutions for the coupled modified Korteweg-de Vries 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":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Coupled modified Korteweg-de Vries equations, Vector localized wave, Dynamical behav- ior, Darboux transformation","lastPublishedDoi":"10.21203/rs.3.rs-4671270/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4671270/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Under investigation in this paper is the coupled modified Korteweg-de Vries equations. 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