Wave Dynamics and Electromagnetic Influences on Propagation in the (3+1)-Dimensional Modified KdV-Zakharov–Kuznetsov Equation: Theoretical Insights and Applications

Wave Dynamics and Electromagnetic Influences on Propagation in the (3+1)-Dimensional Modified KdV-Zakharov–Kuznetsov Equation: Theoretical Insights and Applications | 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 Wave Dynamics and Electromagnetic Influences on Propagation in the (3+1)-Dimensional Modified KdV-Zakharov–Kuznetsov Equation: Theoretical Insights and Applications Khurrem Shehzad, Jun Wang, Muhammad Attique, Muhammad Arshad This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7106076/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 15 You are reading this latest preprint version Abstract This study focuses on understanding wave propagation in dispersive and nonlinear media by analyzing the dynamical behavior of the modified KdV-Zakharov-Kuznetsov (mKdV-ZK) equation. Building on the extensively researched KdV-ZK equation, this paper examines solitary wave solutions of the (3+1)-dimensional mKdV-ZK equation using the newly extended modified Sardar sub-equation method. As a result, a diverse array of novel soliton solutions is obtained, including multi-peak solitons, kink and anti-kink waves, dark and bright solitons, and breather waves. These solitary wave solutions are derived for various physical quantities such as electrostatic field potential, quantum statistical pressures, electric fields, and magnetic fields. The solutions are presented graphically, demonstrating their applicability across numerous domains in physics and other scientific fields. The efficiency of the suggested approach is highlighted, offering potential for solving a wide range of nonlinear wave systems in applied science and mathematical physics. bright soliton modified KdV-ZK equation Kink and anti-kink type waves electric and magnetic fields electrostatic potential Sardar-sub equation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 15 Aug, 2025 Reviews received at journal 10 Aug, 2025 Reviews received at journal 10 Aug, 2025 Reviews received at journal 06 Aug, 2025 Reviewers agreed at journal 18 Jul, 2025 Reviewers agreed at journal 18 Jul, 2025 Reviewers agreed at journal 17 Jul, 2025 Reviewers agreed at journal 17 Jul, 2025 Reviewers agreed at journal 17 Jul, 2025 Reviewers agreed at journal 16 Jul, 2025 Reviewers agreed at journal 16 Jul, 2025 Reviewers invited by journal 16 Jul, 2025 Editor assigned by journal 16 Jul, 2025 Submission checks completed at journal 12 Jul, 2025 First submitted to journal 12 Jul, 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. 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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-7106076","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":487520795,"identity":"f0e15d1c-7975-4678-98e7-86fde07484c7","order_by":0,"name":"Khurrem Shehzad","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYBACCQkow4CBB0iy2QAJxsYDpGhJA2lpIEnLYTAHrxbJ2T1mnysqttmbs/ce/vCj7Lzd2vbDQFtqbKJxaZGWOWM888yZ24k7e84lGPacu5287UwiUMuxtNwGHFrkJHKMGRvbbicY3MgxSOBtu51sdgCohbHhMAEt/27bG9x/Y3Dwb9u5ZLPzD/FrkQZrabjNuOEGj2Ezb9sBO7MbBGyRnJFWzNhw7HbihjM5xswy55ITzG4AbUnA4xeJG8mbGRtqgA47fsb445syO3uz8+kPH3yoscGpBQMkglUmEKscBOxJUTwKRsEoGAUjAwAARKdl1Jnov/UAAAAASUVORK5CYII=","orcid":"","institution":"School of Mathematical Sciences, Jiangsu University","correspondingAuthor":true,"prefix":"","firstName":"Khurrem","middleName":"","lastName":"Shehzad","suffix":""},{"id":487520797,"identity":"b6c13d28-d9b5-44ae-b073-509001a12994","order_by":1,"name":"Jun Wang","email":"","orcid":"","institution":"School of Mathematical Sciences, Jiangsu University","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Wang","suffix":""},{"id":487520799,"identity":"54e4476e-a1fb-44c7-a230-995effa06993","order_by":2,"name":"Muhammad Attique","email":"","orcid":"","institution":"University of Agriculture Faisalabad","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Attique","suffix":""},{"id":487520800,"identity":"aace6871-6d85-4ef9-b1e0-4b0352ae241c","order_by":3,"name":"Muhammad Arshad","email":"","orcid":"","institution":"University of Agriculture Faisalabad","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Arshad","suffix":""}],"badges":[],"createdAt":"2025-07-12 06:23:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7106076/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7106076/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":87153645,"identity":"99c6983a-7dc9-42ee-bda6-1bd8762fa154","added_by":"auto","created_at":"2025-07-21 02:33:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":861330,"visible":true,"origin":"","legend":"","description":"","filename":"ResearchPaperF.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7106076/v1_covered_37524613-a404-445b-94d0-936c43056f81.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Wave Dynamics and Electromagnetic Influences on Propagation in the (3+1)-Dimensional Modified KdV-Zakharov–Kuznetsov Equation: Theoretical Insights and Applications","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":"international-journal-of-applied-and-computational-mathematics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [International Journal of Applied and Computational Mathematics](https://link.springer.com/journal/40819)","snPcode":"40819","submissionUrl":"https://submission.nature.com/new-submission/40819/3","title":"International Journal of Applied and Computational Mathematics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"bright soliton, modified KdV-ZK equation, Kink and anti-kink type waves, electric and magnetic fields, electrostatic potential, Sardar-sub equation","lastPublishedDoi":"10.21203/rs.3.rs-7106076/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7106076/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study focuses on understanding wave propagation in dispersive and nonlinear media by analyzing the dynamical behavior of the modified KdV-Zakharov-Kuznetsov (mKdV-ZK) equation. 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