Bifurcation Analysis and Soliton Structures of Davey-Stewartson Fokas System

Bifurcation Analysis and Soliton Structures of Davey-Stewartson Fokas System | 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 Bifurcation Analysis and Soliton Structures of Davey-Stewartson Fokas System Muhammad Hammad, Amjad Hussain This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6286884/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 In this research, we studied the (2+1)-dimensional Davey-Stewartson Fokas (DS-Fokas) system, which serves as an optimal model for nonlinear pulse propagation in mono-mode optical fibers. We employ the Jacobi elliptic function approach to obtain the novel soliton solutions for the DS-Fokas system. The employed method is a very efficient and robust mathematical approach for solving non-linear models of various nonlinear Schrödinger’s equations (NLSEs) in mathematical physics and sciences. The obtained solutions are useful and significant in elucidating the DS-Fokas system's physical aspects, as they provide insights. Furthermore, we discuss these obtained solutions graphically using 3D and 2D graphs to gain a deep understanding and vision of the analytical results. We also looked at the unpredictable and changing behaviors of the system we studied by using phase portraits, quasi-periodic and chaotic portraits, Poincare maps, bifurcation diagrams, and sensitivity. The theory of planar dynamical systems looks at chaotic patterns in the systems under study when the disturbance term $\cos \omega t$ is added. Numerical simulations demonstrate how changes in frequency and amplitude impact the dynamics of the system. Davey-Stewartson Fokas System Dynamical analysis Chaotic behavior Bifurcation Sensitivity analysis Soliton Solutions Full Text Additional Declarations No competing interests reported. Supplementary Files AnalysisondynamicalsystemofDaveyStewartsonFokasSystem11.zip 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. 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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-6286884","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":481335145,"identity":"65227541-d4a9-4abf-a4d6-7f534ebea042","order_by":0,"name":"Muhammad Hammad","email":"","orcid":"","institution":"Quaid-i-Azam University","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Hammad","suffix":""},{"id":481335146,"identity":"12ae3563-d0c1-4c65-adb8-eba3a4e4b253","order_by":1,"name":"Amjad Hussain","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIiWNgGAWjYFACHijJ3gBmMAIpZiK18BwgUQsDg0QCkVr4G3iPSf74YydjLvl442ceBhvZDQd4Dxvg0yJxgC9NmrctmcdydlqxNA9DmvGGA3zJCXitOcBjJs3YwMxjcDvHAKjlcOKGAzzGB/DpkAdqATqsnsfg5hnj3zwM/wlrMQBqkeBhO8xjcANoHQ/DAbAWvA4zPMxjbM3bdpzH4ExameUcg2TjmYf5kvF6X+54j+HNH3+q7Q2OH958402FnWzf8d7DEvi0IMeBARgxMPPgVIwBYM4hQcsoGAWjYBSMCAAAUMlCbZo3xTEAAAAASUVORK5CYII=","orcid":"","institution":"Quaid-i-Azam University","correspondingAuthor":true,"prefix":"","firstName":"Amjad","middleName":"","lastName":"Hussain","suffix":""}],"badges":[],"createdAt":"2025-03-23 07:08:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6286884/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6286884/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86485622,"identity":"41523060-cb92-4e77-b9a2-3c7bd5078257","added_by":"auto","created_at":"2025-07-11 08:19:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":11010469,"visible":true,"origin":"","legend":"","description":"","filename":"main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6286884/v1_covered_9f42df89-3f0c-4b04-a247-99d8103b8f72.pdf"},{"id":86485090,"identity":"9ea49507-2411-460f-8e8e-134b79b5a7d9","added_by":"auto","created_at":"2025-07-11 08:10:45","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":41107674,"visible":true,"origin":"","legend":"","description":"","filename":"AnalysisondynamicalsystemofDaveyStewartsonFokasSystem11.zip","url":"https://assets-eu.researchsquare.com/files/rs-6286884/v1/ebf08b200b2b427339fcf5b7.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bifurcation Analysis and Soliton Structures of Davey-Stewartson Fokas System","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"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":"Davey-Stewartson Fokas System, Dynamical analysis, Chaotic behavior, Bifurcation, Sensitivity analysis, Soliton Solutions","lastPublishedDoi":"10.21203/rs.3.rs-6286884/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6286884/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this research, we studied the (2+1)-dimensional Davey-Stewartson Fokas (DS-Fokas) system, which serves as an optimal model for nonlinear pulse propagation in mono-mode optical fibers. We employ the Jacobi elliptic function approach to obtain the novel soliton solutions for the DS-Fokas system. The employed method is a very efficient and robust mathematical approach for solving non-linear models of various nonlinear Schrödinger’s equations (NLSEs) in mathematical physics and sciences. The obtained solutions are useful and significant in elucidating the DS-Fokas system's physical aspects, as they provide insights. Furthermore, we discuss these obtained solutions graphically using 3D and 2D graphs to gain a deep understanding and vision of the analytical results. We also looked at the unpredictable and changing behaviors of the system we studied by using phase portraits, quasi-periodic and chaotic portraits, Poincare maps, bifurcation diagrams, and sensitivity. The theory of planar dynamical systems looks at chaotic patterns in the systems under study when the disturbance term $\\cos \\omega t$ is added. 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