Bilinear Feature-Enhanced Symbolic Computation Neural Network Method for Solving the Caudrey-Dodd-Gibbon Equation

Bilinear Feature-Enhanced Symbolic Computation Neural Network Method for Solving the Caudrey-Dodd-Gibbon 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 Article Bilinear Feature-Enhanced Symbolic Computation Neural Network Method for Solving the Caudrey-Dodd-Gibbon Equation Xia Li, Jiang-Long Shen, Jing-Bin Liang, Yu Gao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7734470/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 fifth-order dispersion nonlinear wave Caudrey-Dodd-Gibbon (CDG) equation is a classic model describing soliton phenomena in fields such as plasma magnetosonic waves and optical fiber light pulses, and its exact solution is of great importance for revealing the laws of nonlinear wave motion. In this paper, an integrated framework of ”bilinear polynomial feature enhancement + symbolic computation constraint + neural network learning” is proposed. Bilinear polynomial features such as x 2 , t 2 , and xt are introduced to break through the input limitation of original variables, broaden the boundary of the model in capturing nonlinear interactions between variables, and reduce errors caused by insufficient feature information. Symbolic computation is applied to the bilinear transformation derivation and conservation law analysis of the CDG equation to provide mathematical structure constraints for the neural network, and a collaborative mechanism of ”symbolic reasoning guiding numerical learning” is constructed to improve the interpretability of the model. This framework breaks down the barriers between traditional numerical and pure neural network methods, realizes efficient and accurate solution of the CDG equation, and provides a new path for the study of exact solutions of high-dimensional, variable-coefficient, and strongly nonlinear partial differential equations. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Fifth-order dispersive nonlinear wave equation Bilinearity Feature enhancement Symbolic computation Neural network 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. 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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-7734470","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":534426702,"identity":"7d75e65b-5d41-4eb7-9f21-791b6afb40a0","order_by":0,"name":"Xia Li","email":"","orcid":"","institution":"Yibin University","correspondingAuthor":false,"prefix":"","firstName":"Xia","middleName":"","lastName":"Li","suffix":""},{"id":534426703,"identity":"faa89902-fb34-45af-9322-a7d7088ac31f","order_by":1,"name":"Jiang-Long 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