Degeneration of Solitons for a the (3+1)-dimensional Generalized Nonlinear Evolution Equation for the Shallow Water Waves

Degeneration of Solitons for a the (3+1)-dimensional Generalized Nonlinear Evolution Equation for the Shallow Water Waves | 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 Degeneration of Solitons for a the (3+1)-dimensional Generalized Nonlinear Evolution Equation for the Shallow Water Waves longxing li, Long-Xing Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1179230/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Feb, 2022 Read the published version in Nonlinear Dynamics → Version 1 posted 5 You are reading this latest preprint version Abstract A the (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves is investigated with different methods. Based on symbolic computation and Hirota bilinear form, Nsoliton solutions are constructed. In the process of degeneration of N-soliton solutions, T-breathers are derived by taking complexication method. Then rogue waves will emerge during the degeneration of breathers by taking the parameter limit method. Through full degeneration of N-soliton, M-lump solutions are derived based on long wave limit approach. In addition, we also find out that the partial degeneration of N-soliton process can generate the hybrid solutions composed of soliton, breather and lump. Mechanical Engineering Electrical Engineering Ocean Engineering Applied Mathematics Shallow-water waves T-breather M-lump Hybrid solution Full Text Cite Share Download PDF Status: Published Journal Publication published 14 Feb, 2022 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Major revisions 13 Jan, 2022 Reviews received at journal 18 Dec, 2021 Reviewers invited by journal 18 Dec, 2021 Editor assigned by journal 17 Dec, 2021 First submitted to journal 16 Dec, 2021 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-1179230","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":71063621,"identity":"b6047660-8cc2-4e02-bc76-1669e690139f","order_by":0,"name":"longxing li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYBACPnYQWWHDw8bMfPBBQkUNYS1szCDyTJoMP3tbssGDM8eI1MLYdthGsueMmeTDFmZitPCYSf44c5jH4EZaWkViAxsDf3t3AgEtbGkSEhXpQC3Jx24k7pBhkDhzdgMBLczHJAzOWINtuZF4ho3BQCKXkBbGNonENmaglhyzAiCDGC1AWw62OfOAvM9ApBa2ZMuGM2k8oECWSDhzjIegX/jZewxv/qiwsQdF5ccfFTVy/O29+LUAAYsEMo+HkHIQYP5AjKpRMApGwSgYwQAA2o1Den1p1dYAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-2141-4475","institution":"Qujing Normal University","correspondingAuthor":true,"prefix":"","firstName":"longxing","middleName":"","lastName":"li","suffix":""},{"id":71063622,"identity":"59248e3a-f7cf-49fe-a27c-35f941fc74a4","order_by":1,"name":"Long-Xing Li","email":"","orcid":"","institution":"Qujing Normal University","correspondingAuthor":false,"prefix":"","firstName":"Long-Xing","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2021-12-17 02:35:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1179230/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1179230/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-022-07270-4","type":"published","date":"2022-02-14T14:14:14+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":18196167,"identity":"921822fc-d16a-41d2-a250-18187c05fad0","added_by":"auto","created_at":"2022-02-14 14:14:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1284636,"visible":true,"origin":"","legend":"","description":"","filename":"shallowwaterwavesLi.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1179230/v1_covered.pdf"},{"id":16618931,"identity":"31618b4f-a0a1-4396-ac82-238bebae96c9","added_by":"auto","created_at":"2021-12-20 16:08:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1279767,"visible":true,"origin":"","legend":"","description":"","filename":"shallowwaterwavesLi.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1179230/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eDegeneration of Solitons for a the (3+1)-dimensional Generalized Nonlinear Evolution Equation for the Shallow Water Waves\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1179230/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":true,"isPdf":false,"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":"Shallow-water waves, T-breather, M-lump, Hybrid solution","lastPublishedDoi":"10.21203/rs.3.rs-1179230/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1179230/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA the (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves is investigated with different methods. 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