Interacting chirped localized waves in Bose-Einstein condensates with time-varying complex potentials

Interacting chirped localized waves in Bose-Einstein condensates with time-varying complex potentials | 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 Interacting chirped localized waves in Bose-Einstein condensates with time-varying complex potentials Emmanuel Kengne, WuMing Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6466907/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Jul, 2025 Read the published version in Nonlinear Dynamics → Version 1 posted 11 You are reading this latest preprint version Abstract We examine the interaction of chirp localized matter waves in a cubic-quintic Gross-Pitaevskii equation with variable coefficients (model equation) that governs the dynamics of Bose-Einstein condensates in a time-varying complex potential, which is composed of a parabolic background potential and a gravitational field when the atomic loss/gain is taken into account. By performing a phase imprint transformation, we derive the integrability conditions for the model equation. Under the integrability conditions, the model equation is converted into a nonlinear Schrödinger equation with self-steepening (alias similarity equation). An explicit expression for the growth rate of a purely growing baseband modulational instability is derived for the similarity equation. The criterion of the baseband modulational instability is found to correspond to Bose-Einstein condensates with attractive two-body interatomic interactions. We shown that the gain/loss parameter does not affect the baseband modulational instability. Employing the generalized perturbation (n, N − n)−fold Darboux transformation, new mixed localized wave solutions with nonlinear frequency chirp are built for the model equation. Those solutions helping, we analyze graphically the formation and interaction of chirp localized matter waves in Bose-Einstein condensates with both two-and three-body interactions when the gain/loss of the condensate atoms is taken into consideration. Our results show interactions between various kinds of nonlinear waves such as multi-peak bright/dark solitons, bright/dark breathers, as well as periodic waves. We show that the similarity parameters are useful for controlling the chirped matter localized waves for the model under consideration when the integrability conditions are satisfied. Focusing on the situation when the parameter of the three-body interaction is proportional to that of the two-body interaction, we show that parameter of the two-body interatomic interaction can be used to describe wave compression and also, can be used for the manipulation of chirped localized waves in Bose-Einstein condensates in complicated potential. The spectral parameter is found to be useful for for modeling localized chirped wave structure in the model under consideration. Interestingly, we show that under the integrability conditions, the gain/loss parameter does not affect the wave amplitude during wave propagation (the wave amplitude remains constant during the wave propagation). Chirped localized waves Gross-Pitaevskii equation Bose-Einstein condensate Baseband modulational instability Darboux transformation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 11 Jul, 2025 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 27 May, 2025 Reviews received at journal 20 May, 2025 Reviews received at journal 19 May, 2025 Reviews received at journal 18 May, 2025 Reviewers agreed at journal 29 Apr, 2025 Reviewers agreed at journal 28 Apr, 2025 Reviewers agreed at journal 28 Apr, 2025 Reviewers invited by journal 28 Apr, 2025 Editor assigned by journal 24 Apr, 2025 Submission checks completed at journal 16 Apr, 2025 First submitted to journal 16 Apr, 2025 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. 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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-6466907","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":449499587,"identity":"8276cc46-5ec2-405e-a235-2915364f7da7","order_by":0,"name":"Emmanuel Kengne","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVRIiWNgGAWjYDACHgglx8/AkABiMDYQq8VYsoFULYkGByAMwlr4eQ4fe/h1h02C8fkDzx7zMNjIbjjA/OwBPi2SvW3pxrJn0vLMDhxIN+ZhSDPecIDN3ACfFoPzPGbSkm2Hi80ONqRJ8zAcTtxwgIdNAp8W+/P834Ba/idubmYAaflPWIsBbw+b5Me2A4kb2MBaDhDWInHmmJk0Y1uyscQZhjTJOQbJxjMPs5nh1cLfk/xM8mebnRx//5k0iTcVdrJ9x5uf4dUCAsyQuOFJALoTxCWkHggYf4Ap9gNEqB0Fo2AUjIKRCAB2w0WpxhWBTwAAAABJRU5ErkJggg==","orcid":"","institution":"Zhejiang Normal University","correspondingAuthor":true,"prefix":"","firstName":"Emmanuel","middleName":"","lastName":"Kengne","suffix":""},{"id":449499588,"identity":"2cc5c2cd-c252-407e-98b5-85f97c16607a","order_by":1,"name":"WuMing Liu","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"WuMing","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2025-04-17 01:08:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6466907/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6466907/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-025-11550-0","type":"published","date":"2025-07-11T15:57:51+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":86699558,"identity":"d3713d5f-7568-42cc-a1f7-e3da09643c26","added_by":"auto","created_at":"2025-07-14 16:10:58","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3491290,"visible":true,"origin":"","legend":"","description":"","filename":"KengneetalApril15th2025.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6466907/v1_covered_f973347f-71bd-4974-9895-d5ab6c62649b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Interacting chirped localized waves in Bose-Einstein condensates with time-varying complex potentials","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":"Chirped localized waves, Gross-Pitaevskii equation, Bose-Einstein condensate, Baseband modulational instability, Darboux transformation","lastPublishedDoi":"10.21203/rs.3.rs-6466907/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6466907/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe examine the interaction of chirp localized matter waves in a cubic-quintic Gross-Pitaevskii equation with variable coefficients (model equation) that governs the dynamics of Bose-Einstein condensates in a time-varying complex potential, which is composed of a parabolic background potential and a gravitational field when the atomic loss/gain is taken into account. By performing a phase imprint transformation, we derive the integrability conditions for the model equation. Under the integrability conditions, the model equation is converted into a nonlinear Schrödinger equation with self-steepening (alias similarity equation). An explicit expression for the growth rate of a purely growing baseband modulational instability is derived for the similarity equation. The criterion of the baseband modulational instability is found to correspond to Bose-Einstein condensates with attractive two-body interatomic interactions. We shown that the gain/loss parameter does not affect the baseband modulational instability. Employing the generalized perturbation (n, N − n)−fold Darboux transformation, new mixed localized wave solutions with nonlinear frequency chirp are built for the model equation. Those solutions helping, we analyze graphically the formation and interaction of chirp localized matter waves in Bose-Einstein condensates with both two-and three-body interactions when the gain/loss of the condensate atoms is taken into consideration. Our results show interactions between various kinds of nonlinear waves such as multi-peak bright/dark solitons, bright/dark breathers, as well as periodic waves. We show that the similarity parameters are useful for controlling the chirped matter localized waves for the model under consideration when the integrability conditions are satisfied. Focusing on the situation when the parameter of the three-body interaction is proportional to that of the two-body interaction, we show that parameter of the two-body interatomic interaction can be used to describe wave compression and also, can be used for the manipulation of chirped localized waves in Bose-Einstein condensates in complicated potential. The spectral parameter is found to be useful for for modeling localized chirped wave structure in the model under consideration. Interestingly, we show that under the integrability conditions, the gain/loss parameter does not affect the wave amplitude during wave propagation (the wave amplitude remains constant during the wave propagation).\u003c/p\u003e","manuscriptTitle":"Interacting chirped localized waves in Bose-Einstein condensates with time-varying complex potentials","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-05 04:18:03","doi":"10.21203/rs.3.rs-6466907/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-05-27T19:58:11+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-20T14:36:38+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-19T06:46:45+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-18T12:57:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"223546641415934243926302632481217822844","date":"2025-04-29T06:43:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"29871270563383030421379664396637251929","date":"2025-04-29T03:35:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"230656782362648987538459342430049673132","date":"2025-04-29T02:14:23+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-28T20:45:11+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-04-25T00:04:10+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-17T03:12:06+00:00","index":"","fulltext":""},{"type":"submitted","content":"Nonlinear Dynamics","date":"2025-04-17T01:02:19+00:00","index":"","fulltext":""}],"status":"published","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}}],"origin":"","ownerIdentity":"2e3cd5b3-96ed-4f8d-b056-1bc5e52b3fe7","owner":[],"postedDate":"May 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-07-14T16:07:09+00:00","versionOfRecord":{"articleIdentity":"rs-6466907","link":"https://doi.org/10.1007/s11071-025-11550-0","journal":{"identity":"nonlinear-dynamics","isVorOnly":false,"title":"Nonlinear Dynamics"},"publishedOn":"2025-07-11 15:57:51","publishedOnDateReadable":"July 11th, 2025"},"versionCreatedAt":"2025-05-05 04:18:03","video":"","vorDoi":"10.1007/s11071-025-11550-0","vorDoiUrl":"https://doi.org/10.1007/s11071-025-11550-0","workflowStages":[]},"version":"v1","identity":"rs-6466907","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6466907","identity":"rs-6466907","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}