Optical solitons and other soluions for Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers by an efficient computational technique

Optical solitons and other soluions for Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers by an efficient computational technique | 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 Optical solitons and other soluions for Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers by an efficient computational technique M. Bilal, Mohammad Youins, Aly Ramadan Seadawy, S.T.R. Rizvi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-285910/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Jul, 2021 Read the published version in Optical and Quantum Electronics → Version 1 posted 4 You are reading this latest preprint version Abstract In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan-Kundu-Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations Optical Materials and Devices Photonics/optics Optical soliton RKL equation Generalized exponential rational function method Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Full Text Cite Share Download PDF Status: Published Journal Publication published 22 Jul, 2021 Read the published version in Optical and Quantum Electronics → Version 1 posted Reviewers invited by journal 07 Apr, 2021 Editor invited by journal 07 Mar, 2021 Editor assigned by journal 03 Mar, 2021 First submitted to journal 28 Feb, 2021 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-285910","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":20593914,"identity":"ccac963c-26b7-4491-85a8-e4178fd0562f","order_by":0,"name":"M. Bilal","email":"","orcid":"","institution":"Punjab University: Panjab University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"M.","middleName":"","lastName":"Bilal","suffix":""},{"id":20593915,"identity":"71ba87b8-6fec-40f3-b868-688d5b84f66b","order_by":1,"name":"Mohammad Youins","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVRIiWNgGAWjYJCCDzwMFgz8EmC2hAwxOhhn8DBIMEjOYGBsAGrhIV6LwQ2wFgbCWsylDx9seFMjkbj5dvPxRzdqLHgY2A8f3YBPi2VfWmLjnGMSidvuHEtszjkGdBhPWtoNfFoMzvCYP+ZtAGq5kWPYnMMG1CLBY0ZIi2EzSMvmGSAt/0jRskECqCW3jQgtlj1sYL8Yz7iRljg7t0+Ch42QX8x5mEEhZiPbPyP5wOecb3Vy/OyHj+F3GIYIGz7l2LWMglEwCkbBKEAHAEXaRsgcTl7yAAAAAElFTkSuQmCC","orcid":"","institution":"Jiangsu University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"","lastName":"Youins","suffix":""},{"id":20593916,"identity":"1863174f-a1b2-46b6-b3fe-d24f01e5ec0d","order_by":2,"name":"Aly Ramadan Seadawy","email":"","orcid":"","institution":"Cairo University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Aly","middleName":"Ramadan","lastName":"Seadawy","suffix":""},{"id":20593917,"identity":"5b7bd4d7-7310-4e99-a048-e73cb041dacb","order_by":3,"name":"S.T.R. 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−2.9, γ1 = −4, δ1 = 2, λ1 = 3, θ1 = 4, θ0 = −2, ν = .8.","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/6e25c06614ae2133a0597558.png"},{"id":7905245,"identity":"77b23f70-ca1b-432c-8752-45100f993e9f","added_by":"auto","created_at":"2021-04-12 14:06:41","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":320291,"visible":true,"origin":"","legend":"The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (21), respectively with the parameters k = 1, ω = −4, β2 = 1, α2 = −2, γ2 = −4.6, δ2 = 3, λ2 = 7, θ2 = −3, θ0 = −1, ν = .3.","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/c114d134e4b4f58036faaea5.png"},{"id":7905532,"identity":"dbe86d7c-1948-4273-97e0-ce5aa9b6b405","added_by":"auto","created_at":"2021-04-12 14:09:39","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":256500,"visible":true,"origin":"","legend":"The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (22), respectively with the parameters k = 1, ω = −6, β1 = 1, α1 = −4, γ1 = −2, δ1 = 3, λ1 = 2, θ1 = 6, θ0 = −1, ν = .7.","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/f88578160c7ef00a81b37fe7.png"},{"id":7905530,"identity":"cebe6263-dcd1-4bb6-8f8a-917c1b219349","added_by":"auto","created_at":"2021-04-12 14:09:38","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":276427,"visible":true,"origin":"","legend":"The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (23), respectively with the parameters k = 1, ω = −3.6, β2 = 2, α2 = −3, γ2 = −5, δ2 = 4, λ2 = 8, θ2 = −2, θ0 = −3, ν = .3.","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/faa0354a568368f41cc6c40a.png"},{"id":7905686,"identity":"5dd7cc38-0662-4259-802c-8a0f83625ab0","added_by":"auto","created_at":"2021-04-12 14:12:41","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":379449,"visible":true,"origin":"","legend":"The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (24), respectively with the parameters k = 2, ω = 5, β1 = .5, α1 = 1, γ1 = −5, δ1 = 7, λ1 = 3, θ1 = 5, θ0 = −3, ν = 2.","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/eecf02979293b72f32a28286.png"},{"id":7905246,"identity":"bf57a29c-bb20-485e-8be7-fbd768ef9b91","added_by":"auto","created_at":"2021-04-12 14:06:41","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":300853,"visible":true,"origin":"","legend":"The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (25), respectively with the parameters k = 2, ω = 1, β2 = −3, α2 = 4, γ2 = 0, δ2 = 5, λ2 = 6, θ2 = 7, θ0 = 2, ν = 1.5.","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/c72c7f94f0457df8fd0415f4.png"},{"id":7905531,"identity":"e9120750-3c0d-446d-b202-65380beda6b2","added_by":"auto","created_at":"2021-04-12 14:09:39","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":714565,"visible":true,"origin":"","legend":"The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (27), respectively with the parameters k = 5, ω = −1, β1 = −2, α1 = 1, γ1 = −4, δ1 = 3, λ1 = 2, θ1 = 5, θ0 = 3, ν = .02.","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/274fe23eba9b9169a9890c7f.png"},{"id":7905239,"identity":"e9e2cb3d-9e6b-489f-b6a3-57be9d98eff4","added_by":"auto","created_at":"2021-04-12 14:06:39","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":543907,"visible":true,"origin":"","legend":"The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (28), respectively with the parameters k = 4, ω = 3, β2 = 0, α2 = 3, γ2 = 0, δ2 = 8, λ2 = 2, θ2 = 3, θ0 = 3, ν = .3.","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/722683d4861b5945ada14534.png"},{"id":7905242,"identity":"3812d9a9-3da6-4ab4-9809-c12caec2c9d2","added_by":"auto","created_at":"2021-04-12 14:06:40","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":198365,"visible":true,"origin":"","legend":"The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (34), respectively with the parameters k = 0, ω = −1, β1 = −2, α1 = 1, γ1 = 0, δ1 = −3, λ1 = 5, θ1 = 4, θ0 = 2, ν = 3.","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/86e43f14765f8bea138a5b4a.png"},{"id":7905533,"identity":"9e3aeee0-8e7d-4332-8808-f0e502ed7e5c","added_by":"auto","created_at":"2021-04-12 14:09:40","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":279458,"visible":true,"origin":"","legend":"The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (35), respectively with the parameters k = 1, ω = −4, β2 = −2, α2 = 0, γ2 = −5, δ2 = −2, λ2 = 3, θ2 = 4, θ0 = 2, ν = 1.","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/0f6d4bc621fcde79e972fca8.png"},{"id":7905243,"identity":"78d90cae-fdc1-48ae-bf11-0669a7c14956","added_by":"auto","created_at":"2021-04-12 14:06:41","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":731603,"visible":true,"origin":"","legend":" The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (54), respectively with the parameters k = 8, ω = −2, β1 = −3, α1 = −6, γ1 = −5, δ1 = −4, λ1 = 4, θ1 = 0, θ0 = 1, ν = 1.5.","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/c6a01893aa2a4b2a97dede15.png"},{"id":7905534,"identity":"3475a05f-6881-4062-8e0f-e4407c50a749","added_by":"auto","created_at":"2021-04-12 14:09:41","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":219559,"visible":true,"origin":"","legend":"The (a), (b) and (c) show the 3D, 2D and contour physical behaviour of solution (55), respectively with the parameters k = 0, ω = −4, β2 = −5, α2 = −2, γ2 = −2, δ2 = −2, λ2 = 3, θ2 = 1, θ0 = 0, ν = 1.","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1/13b8c5f6e51629dc363d9f27.png"},{"id":13685228,"identity":"106126b3-040b-4938-8b66-bffbe4145473","added_by":"auto","created_at":"2021-09-17 12:11:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8579101,"visible":true,"origin":"","legend":"","description":"","filename":"Latexsourcefile22.pdf","url":"https://assets-eu.researchsquare.com/files/rs-285910/v1_covered.pdf"},{"id":13619024,"identity":"f0f6d804-9354-4a77-a247-cb58d3f8d9f4","added_by":"auto","created_at":"2021-09-17 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target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"optical-and-quantum-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"oqel","sideBox":"Learn more about [Optical and Quantum Electronics](https://www.springer.com/journal/11082)","snPcode":"11082","submissionUrl":"https://submission.nature.com/new-submission/11082/3","title":"Optical and Quantum Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Optical soliton, RKL equation, Generalized exponential rational function method","lastPublishedDoi":"10.21203/rs.3.rs-285910/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-285910/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan-Kundu-Lakshmanan\nequation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of\nsoliton solutions are also reported. Besides, the physical action of the\nsolution attained are recorded in terms of 3D, 2D and contour\nplots for distinct parameters. The achieved outcomes show that the\napplied computational strategy is direct, efficient, concise and can\nbe implemented in more complex phenomena with the assistant of\nsymbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple\nNLODEs and we have succeeded in a single move to get and\norganize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena\nwith the assistant of symbolic computations","manuscriptTitle":"Optical solitons and other soluions for Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers by an efficient computational technique","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-04-12 14:06:35","doi":"10.21203/rs.3.rs-285910/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewersInvited","content":"","date":"2021-04-08T00:00:00+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Optical and Quantum Electronics","date":"2021-03-08T00:00:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2021-03-04T00:00:00+00:00","index":"","fulltext":""},{"type":"submitted","content":"Optical and Quantum Electronics","date":"2021-02-28T09:36:05+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"optical-and-quantum-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"oqel","sideBox":"Learn more about [Optical and Quantum Electronics](https://www.springer.com/journal/11082)","snPcode":"11082","submissionUrl":"https://submission.nature.com/new-submission/11082/3","title":"Optical and Quantum Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"12f02238-1a3e-4f07-aec5-c3bc3062fb14","owner":[],"postedDate":"April 12th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":3550973,"name":"Optical Materials and Devices"},{"id":3550974,"name":"Photonics/optics"}],"tags":[],"updatedAt":"2021-08-22T15:14:06+00:00","versionOfRecord":{"articleIdentity":"rs-285910","link":"https://doi.org/10.1007/s11082-021-03083-8","journal":{"identity":"optical-and-quantum-electronics","isVorOnly":false,"title":"Optical and Quantum Electronics"},"publishedOn":"2021-07-22 15:02:43","publishedOnDateReadable":"July 22nd, 2021"},"versionCreatedAt":"2021-04-12 14:06:35","video":"","vorDoi":"10.1007/s11082-021-03083-8","vorDoiUrl":"https://doi.org/10.1007/s11082-021-03083-8","workflowStages":[]},"version":"v1","identity":"rs-285910","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-285910","identity":"rs-285910","version":["v1"]},"buildId":"-HB7Z8yhvgn0wM9Nzuekk","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}