A new composite technique to obtain non-traveling wave solutions of the (2+1)-dimensional extended variable coefficients Bogoyavlenskii-Kadomtsev-Petviashvili equation

A new composite technique to obtain non-traveling wave solutions of the (2+1)-dimensional extended variable coefficients Bogoyavlenskii-Kadomtsev-Petviashvili equation | 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 A new composite technique to obtain non-traveling wave solutions of the (2+1)-dimensional extended variable coefficients Bogoyavlenskii-Kadomtsev-Petviashvili equation Xiaoxiao Zheng, Lingling Zhao, Yuanqing Xu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2372856/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Apr, 2023 Read the published version in Qualitative Theory of Dynamical Systems → Version 1 posted 7 You are reading this latest preprint version Abstract In this article, we investigate non-traveling wave solutions for the (2+1)-dimensional extended variable coefficients Bogoyavlenskii-Kadomtsev-Petviashvili equation with time-dependent coefficients (VC-BKP). Inspired by Prof. Shang, we apply the extended three-wave method and the generalized variable separation method to the investigated problem for the first time in this article. The technique is effective, easily applicable, and reliable in solving non-traveling wave solutions. We successfully obtain forty-four exact non-traveling solutions, including double periodic solutions, kinky breather wave solution, periodic cross-kink solution and some new exact non-traveling solutions obtained firstly in this paper. These results all have a tail which gives a prediction of physical phenomenon. Moreover, we discuss the arbitrary coefficients of solutions in the real, purely imaginary and complex domains, which greatly enriches the forms of solutions. The dynamic phenomena of four types of exact solutions are demonstrated by contour, 2D and 3D graphics, which help to show their physical interpretation. 2010 Mathematics Subject Classification 35C99, 35G20, 37K10, 68W30 Extended three-wave method generalized variable separation method eVC-BKP equation non-traveling solutions Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 11 Apr, 2023 Read the published version in Qualitative Theory of Dynamical Systems → Version 1 posted Editorial decision: Major revision 13 Jan, 2023 Reviews received at journal 20 Dec, 2022 Reviewers agreed at journal 14 Dec, 2022 Reviewers invited by journal 14 Dec, 2022 Editor assigned by journal 13 Dec, 2022 Submission checks completed at journal 13 Dec, 2022 First submitted to journal 13 Dec, 2022 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-2372856","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":159795942,"identity":"0ab13a28-6853-4667-987e-62b64e670621","order_by":0,"name":"Xiaoxiao Zheng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBElEQVRIiWNgGAWjYDACZhBhAMQSIEbFfzk29vYDpGg5w2zMx3MmgUjrQFoY25gT50k4GOBVaHCc+eFjngI7OfnZzccefjnDlt4mwZDA8KNiG04tks1sxoYzDJKNGeccSzeWqeDJbZNuPMDYc+Y2Ti38zAxmEh8MmBObJXLMpCXOSOS2yRxIYGZsw62FjZn9m0SCQX1im0T+N2nJNoN0NiAXrxZ+Zh6QLYcTeyRy2CQ/tiUkENQi2cxTDPTLcWMJiTQzaYYzBwzbgIF8EJ9fDM4f3/iY50+1nPyM5GeSPyoOyMu3tx988KMCtxYUwMwDZRwgTj0QMP4gWukoGAWjYBSMJAAAiQFP0ofC4yYAAAAASUVORK5CYII=","orcid":"","institution":"Qufu Normal University","correspondingAuthor":true,"prefix":"","firstName":"Xiaoxiao","middleName":"","lastName":"Zheng","suffix":""},{"id":159795943,"identity":"ae91d76f-9421-4500-9b46-e6bb0a2be3a7","order_by":1,"name":"Lingling Zhao","email":"","orcid":"","institution":"Qufu Normal University","correspondingAuthor":false,"prefix":"","firstName":"Lingling","middleName":"","lastName":"Zhao","suffix":""},{"id":159795944,"identity":"094570cb-0cc6-48cc-90ff-d7dec8d467fa","order_by":2,"name":"Yuanqing Xu","email":"","orcid":"","institution":"Qufu Normal University","correspondingAuthor":false,"prefix":"","firstName":"Yuanqing","middleName":"","lastName":"Xu","suffix":""}],"badges":[],"createdAt":"2022-12-13 07:44:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2372856/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2372856/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s12346-023-00775-2","type":"published","date":"2023-04-11T20:28:34+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":44727773,"identity":"17b55723-0604-457d-9e04-08fa6007d0fc","added_by":"auto","created_at":"2023-10-16 20:55:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":902171,"visible":true,"origin":"","legend":"","description":"","filename":"Anewcompositetechniquetoobtainnontravelingwavesolutionsofthe21dimensionalextendedvariablecoefficientsBogoyavlenskiiKadomtsevPetviashviliequation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2372856/v1_covered_82dd1a05-7321-4d76-8c46-a1fb5a774e95.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A new composite technique to obtain non-traveling wave solutions of the (2+1)-dimensional extended variable coefficients Bogoyavlenskii-Kadomtsev-Petviashvili equation","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":"qualitative-theory-of-dynamical-systems","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qtds","sideBox":"Learn more about [Qualitative Theory of Dynamical Systems](http://link.springer.com/journal/12306)","snPcode":"12346","submissionUrl":"https://submission.nature.com/new-submission/12346/3","title":"Qualitative Theory of Dynamical Systems","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Extended three-wave method, generalized variable separation method, eVC-BKP equation, non-traveling solutions","lastPublishedDoi":"10.21203/rs.3.rs-2372856/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2372856/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this article, we investigate non-traveling wave solutions for the (2+1)-dimensional extended variable coefficients Bogoyavlenskii-Kadomtsev-Petviashvili equation with time-dependent coefficients (VC-BKP). Inspired by Prof. Shang, we apply the extended three-wave method and the generalized variable separation method to the investigated problem for the first time in this article. The technique is effective, easily applicable, and reliable in solving non-traveling wave solutions. We successfully obtain forty-four exact non-traveling solutions, including double periodic solutions, kinky breather wave solution, periodic cross-kink solution and some new exact non-traveling solutions obtained firstly in this paper. These results all have a tail which gives a prediction of physical phenomenon. Moreover, we discuss the arbitrary coefficients of solutions in the real, purely imaginary and complex domains, which greatly enriches the forms of solutions. The dynamic phenomena of four types of exact solutions are demonstrated by contour, 2D and 3D graphics, which help to show their physical interpretation.\u003c/p\u003e\n\u003cp\u003e2010 Mathematics Subject Classification 35C99, 35G20, 37K10, 68W30\u003c/p\u003e","manuscriptTitle":"A new composite technique to obtain non-traveling wave solutions of the (2+1)-dimensional extended variable coefficients Bogoyavlenskii-Kadomtsev-Petviashvili equation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-12-15 10:39:34","doi":"10.21203/rs.3.rs-2372856/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2023-01-13T05:22:56+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2022-12-20T05:51:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"50e06ca6-5017-4912-b4ad-ccd990ddf34d","date":"2022-12-14T07:23:26+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-12-14T07:10:01+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-12-13T15:00:12+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2022-12-13T14:53:07+00:00","index":"","fulltext":""},{"type":"submitted","content":"Qualitative Theory of Dynamical Systems","date":"2022-12-13T07:39:15+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"qualitative-theory-of-dynamical-systems","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qtds","sideBox":"Learn more about [Qualitative Theory of Dynamical Systems](http://link.springer.com/journal/12306)","snPcode":"12346","submissionUrl":"https://submission.nature.com/new-submission/12346/3","title":"Qualitative Theory of Dynamical Systems","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"4bfe3a13-88ce-47fa-b66b-1633444a6df2","owner":[],"postedDate":"December 15th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-10-16T20:46:07+00:00","versionOfRecord":{"articleIdentity":"rs-2372856","link":"https://doi.org/10.1007/s12346-023-00775-2","journal":{"identity":"qualitative-theory-of-dynamical-systems","isVorOnly":false,"title":"Qualitative Theory of Dynamical Systems"},"publishedOn":"2023-04-11 20:28:34","publishedOnDateReadable":"April 11th, 2023"},"versionCreatedAt":"2022-12-15 10:39:34","video":"","vorDoi":"10.1007/s12346-023-00775-2","vorDoiUrl":"https://doi.org/10.1007/s12346-023-00775-2","workflowStages":[]},"version":"v1","identity":"rs-2372856","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2372856","identity":"rs-2372856","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}