PT-symmetric KdV Solutions and Their Algebraic Extension with Zero-Width Resonances

PT-symmetric KdV Solutions and Their Algebraic Extension with Zero-Width Resonances | 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 Article PT-symmetric KdV Solutions and Their Algebraic Extension with Zero-Width Resonances Kumar Abhinav, Aradhya Shukla, Prasanta Kumar Panigrahi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4148950/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract A class of complex breather and soliton solutions to both KdV and mKdV equations are identified with a Pöschl-Teller type PT-symmetric potential. However, these solutions represent only the unbroken-PT phase owing to their isospectrality to an infinite potential well in the complex plane having real spectra. To obtain the broken-PT phase, an extension of the potential satisfying the sl (2,ℝ) potential algebra is mandatory that additionally supports non-trivial zero-width resonances. Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Nonlinear phenomena Physical sciences/Physics/Quantum physics/Theoretical physics Physical sciences/Physics/Quantum physics/Quantum mechanics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 04 Jun, 2024 Reviews received at journal 01 Jun, 2024 Reviewers agreed at journal 30 May, 2024 Reviews received at journal 30 May, 2024 Reviewers agreed at journal 30 May, 2024 Reviewers invited by journal 29 Apr, 2024 Editor assigned by journal 06 Apr, 2024 Editor invited by journal 02 Apr, 2024 Submission checks completed at journal 02 Apr, 2024 First submitted to journal 22 Mar, 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. 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-4148950","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":286922323,"identity":"da96f505-1dd9-47d2-b2f7-8fd0324c5b4e","order_by":0,"name":"Kumar Abhinav","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYBACCSidYMDewMDMYMDMwAcROECEFp4DEC1sED4xWiQSgFoYiNAiOSM78XMFg12eueTrxM8FBdZybAzMDz8w/riDU4u0RO5myTMMycWWs3M3S88wSDdmY2AzlmBIeIZTi5xE7gZJoMcTN9zO3SDNY3A4sY2BwQzosMP4tGz+2cBQn7jh5tnNvyFa2L/h1QJ02DagLYcTN9zg3Qa1hQe/LZI9b7dZNhgcLzY4k7vNmgfkF2aeYomENNxaJI7nbr7ZUFGdZ3D87ObbPH+s5fjZ2zd++GCDWwsEGCBzgLHDkEBAwygYBaNgFIwC/AAAVm5PNkf5SH0AAAAASUVORK5CYII=","orcid":"","institution":"Mahidol University","correspondingAuthor":true,"prefix":"","firstName":"Kumar","middleName":"","lastName":"Abhinav","suffix":""},{"id":286922324,"identity":"d2259d7b-9bc9-4d1a-ba95-a687bb48ef4f","order_by":1,"name":"Aradhya Shukla","email":"","orcid":"","institution":"GLA University","correspondingAuthor":false,"prefix":"","firstName":"Aradhya","middleName":"","lastName":"Shukla","suffix":""},{"id":286922325,"identity":"c3f275be-5026-4ae2-93de-7a77500bc9ad","order_by":2,"name":"Prasanta Kumar Panigrahi","email":"","orcid":"","institution":"Siksha O Anusandhan University","correspondingAuthor":false,"prefix":"","firstName":"Prasanta","middleName":"Kumar","lastName":"Panigrahi","suffix":""}],"badges":[],"createdAt":"2024-03-22 10:20:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4148950/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4148950/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":54171077,"identity":"b10c84a6-6585-44bc-a140-591a8023a1e9","added_by":"auto","created_at":"2024-04-05 14:38:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":739635,"visible":true,"origin":"","legend":"","description":"","filename":"KdVFromPTSciRep.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4148950/v1_covered_1881270c-6f31-4332-a977-adcc31305bab.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"PT-symmetric KdV Solutions and Their Algebraic Extension with Zero-Width Resonances","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4148950/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4148950/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA class of complex breather and soliton solutions to both KdV and mKdV equations are identified with a Pöschl-Teller type\u0026nbsp;PT-symmetric potential. 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