New solitons and breather-like solutions to a (2+1)-dimensional coupled variable-coefficient Schrödinger equation in optical fibers

New solitons and breather-like solutions to a (2+1)-dimensional coupled variable-coefficient Schrödinger equation in optical fibers | 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 New solitons and breather-like solutions to a (2+1)-dimensional coupled variable-coefficient Schrödinger equation in optical fibers Xingye Wang, Ben Gao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4490406/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Jun, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted 16 You are reading this latest preprint version Abstract The nonlinear Schrödinger equation is an important theoretical model for ultra-long and ultra-fast transportation. Therefore, the situation of its normal propagation and collision has significant implications for practical applications. However, current researchs mostly focus on solutions of one dimensional or two dimensional Schrödinger equations with constant coefficients. Although these solutions possess good properties, they are often too unilateral. In this paper, our research mainly focuses on solutions of a (2+1)-dimensional coupled variable-coefficient Schrödinger equation. Through a explicit transformation, the solutions of this equation in the form of one-soliton, two-soliton, three-soliton, and bright-dark-soliton-breather-like waves can be acquired by utilizing the developed Hirota bilinear method. Furthermore, we will explicate that the collisions among two-soliton, bright-dark-two-breather-like are elastic with the help of the asymptotic analysis method. At last, we will exhibit their collisions via illustrations. (2+1)-dimensional coupled variable-coefficient Schrödinger equation Soliton solutions Breather-like solutions developed Hirota bilinear method Asymptotic analysis method Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 23 Jun, 2024 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 07 Jun, 2024 Reviews received at journal 07 Jun, 2024 Reviews received at journal 06 Jun, 2024 Reviewers agreed at journal 01 Jun, 2024 Reviewers agreed at journal 01 Jun, 2024 Reviewers agreed at journal 01 Jun, 2024 Reviewers agreed at journal 01 Jun, 2024 Reviewers agreed at journal 01 Jun, 2024 Reviewers agreed at journal 01 Jun, 2024 Reviewers agreed at journal 01 Jun, 2024 Reviewers agreed at journal 01 Jun, 2024 Reviewers agreed at journal 01 Jun, 2024 Reviewers invited by journal 01 Jun, 2024 Editor assigned by journal 01 Jun, 2024 Submission checks completed at journal 30 May, 2024 First submitted to journal 28 May, 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. 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-4490406","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":311941397,"identity":"c875b627-6681-489a-8293-579efad28637","order_by":0,"name":"Xingye Wang","email":"","orcid":"","institution":"Taiyuan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Xingye","middleName":"","lastName":"Wang","suffix":""},{"id":311941398,"identity":"83997eca-c98b-434d-8b32-9cb35c278edf","order_by":1,"name":"Ben Gao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxUlEQVRIiWNgGAWjYBACAxCRYCDBw8/e2PjwA/FaKixkJHsONxtLEK2F4UyFjcGM9DYBHmK0mLP3Hv7wsE2Cx0DyYRuDBIOdnG4DAS2WPecSDBKBWsylE9seFDAkG5sdIOSwGzkGCSAtlrMT2w0kGA4kbiOo5f4bgwMgLQY3DwJJorTc4DFsSDgD1HKDkUgtlj05xsBAluCR7EkEBrIBEX4xZz9j/PGHQZ09P/vxhw8/VNjJEdSC7k7SlI+CUTAKRsEowAEAzmVAlNDJD1wAAAAASUVORK5CYII=","orcid":"","institution":"Taiyuan University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Ben","middleName":"","lastName":"Gao","suffix":""}],"badges":[],"createdAt":"2024-05-28 11:08:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4490406/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4490406/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-024-09910-3","type":"published","date":"2024-06-24T00:36:09+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":58976525,"identity":"6ed51ac4-a5f6-4661-a47c-95d080e944e6","added_by":"auto","created_at":"2024-06-25 00:36:16","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1694320,"visible":true,"origin":"","legend":"","description":"","filename":"document.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4490406/v1_covered_c6ad1f1b-60cf-400a-ab09-863ecff28769.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"New solitons and breather-like solutions to a (2+1)-dimensional coupled variable-coefficient Schrödinger equation in optical fibers","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"(2+1)-dimensional coupled variable-coefficient Schrödinger equation, Soliton solutions, Breather-like solutions, developed Hirota bilinear method, Asymptotic analysis method","lastPublishedDoi":"10.21203/rs.3.rs-4490406/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4490406/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The nonlinear Schrödinger equation is an important theoretical model for ultra-long and ultra-fast transportation. Therefore, the situation of its normal propagation and collision has significant implications for practical applications. However, current researchs mostly focus on solutions of one dimensional or two dimensional Schrödinger equations with constant coefficients. Although these solutions possess good properties, they are often too unilateral. In this paper, our research mainly focuses on solutions of a (2+1)-dimensional coupled variable-coefficient Schrödinger equation. Through a explicit transformation, the solutions of this equation in the form of one-soliton, two-soliton, three-soliton, and bright-dark-soliton-breather-like waves can be acquired by utilizing the developed Hirota bilinear method. Furthermore, we will explicate that the collisions among two-soliton, bright-dark-two-breather-like are elastic with the help of the asymptotic analysis method. At last, we will exhibit their collisions via illustrations.","manuscriptTitle":"New solitons and breather-like solutions to a (2+1)-dimensional coupled variable-coefficient Schrödinger equation in optical fibers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-12 04:02:42","doi":"10.21203/rs.3.rs-4490406/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-06-07T22:01:01+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-07T16:18:50+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-06T06:46:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"82027809079463677545872819254886876188","date":"2024-06-02T02:48:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"161168682015984711187479048004271053755","date":"2024-06-01T23:42:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"101787001215152076454387613705500540124","date":"2024-06-01T23:09:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"279889226173649711578194189752154614370","date":"2024-06-01T23:07:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"217565569385870236589763996104818441166","date":"2024-06-01T21:12:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"88578339057275580441740090909829330911","date":"2024-06-01T18:17:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"266368318923047711666726698427665654496","date":"2024-06-01T17:32:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"29330614265377096110762252150851928823","date":"2024-06-01T17:31:16+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"264465723201456722153348892306269019366","date":"2024-06-01T17:29:02+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-06-01T17:25:59+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-06-01T14:09:02+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-05-30T21:24:50+00:00","index":"","fulltext":""},{"type":"submitted","content":"Nonlinear Dynamics","date":"2024-05-28T11:07:09+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":"c565d894-eb9a-47bf-9842-42ad23bd0648","owner":[],"postedDate":"June 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-06-25T00:36:09+00:00","versionOfRecord":{"articleIdentity":"rs-4490406","link":"https://doi.org/10.1007/s11071-024-09910-3","journal":{"identity":"nonlinear-dynamics","isVorOnly":false,"title":"Nonlinear Dynamics"},"publishedOn":"2024-06-24 00:36:09","publishedOnDateReadable":"June 24th, 2024"},"versionCreatedAt":"2024-06-12 04:02:42","video":"","vorDoi":"10.1007/s11071-024-09910-3","vorDoiUrl":"https://doi.org/10.1007/s11071-024-09910-3","workflowStages":[]},"version":"v1","identity":"rs-4490406","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4490406","identity":"rs-4490406","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}