An investigation on explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

An investigation on explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation | 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 An investigation on explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation Qianqian Guo, Xiaoming Peng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3895886/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper is devoted to investigating new non-traveling wave solutions for the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation. By using the generalized variable separation method and extended three-wave approach, the process of solving the (3+1)-dimensional potential-YTSF equation is simplified and the interactions of multiple waves are revealed. With the aid of Maple, we derive thirty-six types new exact explicit non-traveling wave solutions with a like-parabolic tail. The main characteristic of these solutions is that they contain three arbitrary functions, which greatly enrich the diversity of solutions. This characteristic shows the novelty of our work. In particular, selecting suitable arbitrary functions, we can obtain traveling solutions, such as kink-wave solutions, solitary-wave solutions, kinky breather-wave solutions, singular solutions and periodic solutions. Then, some dynamical phenomena are exhibited by 3D representation, providing the complicated structure of the non-traveling wave solutions for the (3+1) dimensional potential-YTSF equation and their physical interpretation. In addition, our findings improve and extend the existing literature on related topics. Explicit exact solutions Non-traveling wave solutions Variable separation method Potential-YTSF equation Three-wave approach Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-3895886","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":270112431,"identity":"8adbb60e-9239-40b8-808b-d9112a38e507","order_by":0,"name":"Qianqian Guo","email":"","orcid":"","institution":"Guangdong University Of Finances and Economics","correspondingAuthor":false,"prefix":"","firstName":"Qianqian","middleName":"","lastName":"Guo","suffix":""},{"id":270112432,"identity":"0c99b45f-fad8-4553-89b4-5b931695cd5a","order_by":1,"name":"Xiaoming Peng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4UlEQVRIiWNgGAWjYPACGwaGA4wPgAxmorWkAbUwG5Ck5TAJWszZew+/5s05b9d3IxnosgrrxAb2swfwarHsOZdmOXPb7eSZN5KB1pxJT2zgyUvAq8XgRo6ZwUegFoMb+cckGNsOJzZI8Bjg13L/jZlB4rZzQC3J7D8Y/xGj5QaP8YOP2w7YAbWwMTA2EKHFsifHjHHmtuQEyTOPmSUSjqUbt/Hk4Ndizn7G+DPvNjt7vuPJjB8+1FjL9rOfIeAwBgY2CSCd2ADiJQAxG171EC3MH4C0PSGFo2AUjIJRMIIBAC/WSP88PdswAAAAAElFTkSuQmCC","orcid":"","institution":"Guangdong University Of Finances and Economics","correspondingAuthor":true,"prefix":"","firstName":"Xiaoming","middleName":"","lastName":"Peng","suffix":""}],"badges":[],"createdAt":"2024-01-25 03:44:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3895886/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3895886/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50530133,"identity":"241111b2-8e0f-40bb-b8ea-9a50edcca67e","added_by":"auto","created_at":"2024-02-02 01:58:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":920699,"visible":true,"origin":"","legend":"","description":"","filename":"snarticletemplate.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3895886/v1_covered_72ec1626-dc4c-4208-9da9-9a394d5e3c5f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An investigation on explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Explicit exact solutions, Non-traveling wave solutions, Variable separation method, Potential-YTSF equation, Three-wave approach","lastPublishedDoi":"10.21203/rs.3.rs-3895886/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3895886/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper is devoted to investigating new non-traveling wave solutions for the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation. 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