On the Theory of Nonlinear Exterior Integration: A Constructive Differential Algebraic Framework

On the Theory of Nonlinear Exterior Integration: A Constructive Differential Algebraic Framework | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 20 October 2025 V1 Latest version Share on On the Theory of Nonlinear Exterior Integration: A Constructive Differential Algebraic Framework Authors : Dongqi Liu 0009-0006-4018-9292 and shifa liu 0009-0003-6570-2812 [email protected] Authors Info & Affiliations 194 views 143 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract 本文发展了非线性外积分的综合理论，作为微分几何中经典外积分的推广。在非线性偏微分方程的建设性框架和成熟的外微积分理论的基础上，我们通过微分代数中的递归附加过程定义了非线性外积分算子。本文提出了非线性外积分的详细数学公式、基本属性、计算方法和几何应用，特别强调其与非线性斯托克斯定理和非线性规范理论中特征类的关系。提供了几个说明性示例和严格的证明来证明该理论的一致性和实用性。该框架扩展了经典的外部积分以处理非线性微分形式，并为非线性场论中的降维提供了新的工具。 Supplementary Material File (nonlinear_exterior_integration.pdf) Download 421.92 KB Information & Authors Information Version history V1 Version 1 20 October 2025 DOI 10.22541/au.176099574.45271540/v1 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords characteristic classes differential algebraic closure differential forms dimensional reduction exterior derivative fiber bundles nonlinear exterior integration nonlinear pdes stokes theorem Authors Affiliations Dongqi Liu 0009-0006-4018-9292 View all articles by this author shifa liu 0009-0003-6570-2812 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 194 views 143 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Dongqi Liu, shifa liu. 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