Exact Solitary Wave Solutions of the Generalized Strain Wave Equation in Microstructured Solids and their Impacts on Waveguide Properties via the iB-Function Method

Exact Solitary Wave Solutions of the Generalized Strain Wave Equation in Microstructured Solids and their Impacts on Waveguide Properties via the iB-Function 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 Solitary Wave Solutions of the Generalized Strain Wave Equation in Microstructured Solids and their Impacts on Waveguide Properties via the iB-Function Method Stallon Mezezem Songna, Jean Roger Bogning, Francois Beceau Pelap This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8752965/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 In this work, we employ the implicit Bogning (iB) function method to obtain exact solitary wave solutions in various forms of the generalized strain wave equation in microstructured solids. We investigate the impact of these microstructures on the obtained solutions and introduce new varieties of waveguides via the reduced partial differential equations governing wave propagation. The microstructures are considered solely from a waveguide perspective. To carry out the study, we constructed the wave solutions of nonlinear partial differential equation governing the dynamics in solid microstructures. The control microstructured solids are assumed to be immersed in a medium with variable coefficients. Using the characteristic indices of the iB functions, we determine the forms of the solutions and evaluate the influence of each coefficients. Some solutions dynamics are illustrated graphically through three-dimensional profiles. Our results differ significantly from earlier findings and have not been published elsewhere. They demonstrate that the iB function method is an effective and straightforward mathematical tool for obtaining exact solitary solutions to nonlinear partial differential equations arising in the mathematical physics, materials physics, fiber optics, engineering, and other natural sciences. Generalized strain wave equation microstructured solid implicit Bogning functions waveguide impacts solitary wave Full Text Additional Declarations No competing interests reported. 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. 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-8752965","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":593562166,"identity":"c7025354-5304-430c-a144-1b95442dbcbb","order_by":0,"name":"Stallon Mezezem Songna","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7klEQVRIiWNgGAWjYHACxgMPYMwPQMzGTkgDGwPDgQSY5hkgAWZStDDzgEkCOuTnNz84kFBxJ5qf//DRzTa/tsnzMTMwfviYg1uLwTE2gwMJZ57lzmw4lnY7t++2YRszA7PkzG14tLAxGBxIbDucu+Fgj9nt3J7bjEAtbMy8eLTIt7F/AGvZf5j/223Lntv2BLUwHOOB2sLGw3ab4cftRIJaDI7lFAD9cjh3xhk2s5u9DbeT25gZm/H6Rb75+MYHHyoO5/b3H35248ef27bz25sPfviIz2EogLENTDYQqx4E/pCieBSMglEwCkYKAABxJ1nE0OsRMQAAAABJRU5ErkJggg==","orcid":"","institution":"Université de Dschang","correspondingAuthor":true,"prefix":"","firstName":"Stallon","middleName":"Mezezem","lastName":"Songna","suffix":""},{"id":593562167,"identity":"cfb7d896-f1fd-4607-88f7-f98f7454ddb0","order_by":1,"name":"Jean Roger Bogning","email":"","orcid":"","institution":"University of Bamenda","correspondingAuthor":false,"prefix":"","firstName":"Jean","middleName":"Roger","lastName":"Bogning","suffix":""},{"id":593562168,"identity":"919b2798-2e03-4eca-bea6-e65be1f5bc45","order_by":2,"name":"Francois Beceau Pelap","email":"","orcid":"","institution":"Université de Dschang","correspondingAuthor":false,"prefix":"","firstName":"Francois","middleName":"Beceau","lastName":"Pelap","suffix":""}],"badges":[],"createdAt":"2026-02-01 00:38:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8752965/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8752965/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103050554,"identity":"f6b24215-5502-4d09-af30-d97365b0e411","added_by":"auto","created_at":"2026-02-20 07:50:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":889673,"visible":true,"origin":"","legend":"","description":"","filename":"mezezemalIJTP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8752965/v1_covered_9cdbfc16-6c3f-48d7-bcd8-8ca09d98a1bc.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Exact Solitary Wave Solutions of the Generalized Strain Wave Equation in Microstructured Solids and their Impacts on Waveguide Properties via the iB-Function Method","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","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":"Generalized strain wave equation, microstructured solid, implicit Bogning functions, waveguide impacts, solitary wave","lastPublishedDoi":"10.21203/rs.3.rs-8752965/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8752965/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eIn this work, we employ the implicit Bogning (iB) function method to obtain exact solitary wave solutions in various forms of the generalized strain wave equation in microstructured solids. 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