Exact Solitonic Solutions in New Hamiltonian Amplitude Equation using Riccati-Bernoulli Method

Exact Solitonic Solutions in New Hamiltonian Amplitude Equation using Riccati-Bernoulli Method | 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 Exact Solitonic Solutions in New Hamiltonian Amplitude Equation using Riccati-Bernoulli Method jibrin sale Yusuf This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7415978/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 The propagation of optical pulses in nonlinear media is a complex phenomenon that requires accurate modeling and analysis. The New Hamiltonian Amplitude Equation (HNLS) is a fundamental model that describes this phenomenon, but solving it exactly is a challenging task. We employ the Riccati-Bernoulli Sub ODE method to derive exact soliton solutions to the HNLS. This research contributes to the understanding of optical soliton dynamics in various nonlinear regimes, providing a foundation for the development of novel optical communication systems and devices. We use the Riccati-Bernoulli Sub ODE method to derive exact soliton solutions to the HNLS. The method is applied to various nonlinear regimes, including Kerr law, Quadratic Cubic, and Parabolic law nonlinearities. Additionally, we obtain particular solutions using the power series method. The resulting optical soliton solutions are expressed in terms of various mathematical functions, including trigonometric functions, hyperbolic functions, exponential functions, and rational functions. These solutions describe the oscillatory behavior, exponential growth or decay, rapid growth or decay, and algebraic decay or growth of optical pulses in various nonlinear regimes. The solutions obtained using the power series method provide further insight into the behavior of optical pulses in these regimes. Our results provide a comprehensive understanding of optical soliton dynamics in nonlinear media. New Hamiltonian Amplitude Equation Kerr law Quadratic Cubic and Parabolic law Full Text Additional Declarations The authors declare no competing interests. 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. 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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-7415978","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":503031051,"identity":"0a6e9e81-36b9-4234-92d2-d3d7373164b5","order_by":0,"name":"jibrin sale Yusuf","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIie2PMQuCQBTH33FwLpetioVfwXAuv4ri2hC0FIEVwmt07ZPcXAg5tQcuWV8gh6C2zqZa1DHofsPBO96P9/8DKBQ/CIk5gD8B0IGsz/KD6+0UB4ABjZ1KYc13pAJvRUOjmhsVuukcbmcnspm2xvl9POrJc8XlVBtMD7e+kw6Q7zHvi1AGY647ru/iyi47gkaAuSmoVDizWiiRh3aBU1MsWys0QIMgKUXaRtFDqaQh8iC2iMg4ow1dBskxJY9ZNEy0rCifYuF1tbi41iqrj4Hy91uzXmF/pXw0bCsUCsV/8gJWUz9bEi/NYwAAAABJRU5ErkJggg==","orcid":"","institution":"Federal University Dutse","correspondingAuthor":true,"prefix":"","firstName":"jibrin","middleName":"sale","lastName":"Yusuf","suffix":""}],"badges":[],"createdAt":"2025-08-20 09:45:39","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-7415978/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7415978/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":89553852,"identity":"e9f95ca1-2baf-46c8-b3ca-a3a975749292","added_by":"auto","created_at":"2025-08-21 08:58:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":621085,"visible":true,"origin":"","legend":"","description":"","filename":"Hamiltonian.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7415978/v1_covered_8f014e55-4f2f-4e2e-8d1d-d62633954298.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eExact Solitonic Solutions in New Hamiltonian Amplitude Equation using Riccati-Bernoulli Method\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Federal University Dutse ","isAcceptedByJournal":false,"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":"New Hamiltonian Amplitude Equation, Kerr law, Quadratic Cubic and Parabolic law","lastPublishedDoi":"10.21203/rs.3.rs-7415978/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7415978/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe propagation of optical pulses in nonlinear media is a complex phenomenon that requires accurate modeling and analysis. The New Hamiltonian Amplitude Equation (HNLS) is a fundamental model that describes this phenomenon, but solving it exactly is a challenging task. We employ the Riccati-Bernoulli Sub ODE method to derive exact soliton solutions to the HNLS. This research contributes to the understanding of optical soliton dynamics in various nonlinear regimes, providing a foundation for the development of novel optical communication systems and devices.\u003c/p\u003e\n\u003cp\u003eWe use the Riccati-Bernoulli Sub ODE method to derive exact soliton solutions to the HNLS. The method is applied to various nonlinear regimes, including Kerr law, Quadratic Cubic, and Parabolic law nonlinearities. Additionally, we obtain particular solutions using the power series method.\u003c/p\u003e\n\u003cp\u003eThe resulting optical soliton solutions are expressed in terms of various mathematical functions, including trigonometric functions, hyperbolic functions, exponential functions, and rational functions. 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