Towards a theory of homotopy structures for differential equations: First definitions and examples

被引：0

作者：

Magnot, Jean-Pierre ^{[1
,2
]}

Reyes, Enrique G. ^{[3
]}

Rubtsov, Vladimir ^{[1
,4
,5
]}

机构：

[1] Univ Angers, CNRS, LAREMA, SFR MATHSTIC, F-49000 Angers, France

[2] Lycee Jeanne Arc, Ave Grande Bretagne, F-63000 Clermont Ferrand, France

[3] Univ Santiago Chile USACH, Dept Matemat & Ciencia Comp, Casilla 307 Correo 2, Santiago, Chile

[4] IGAP, Via Beirut 2, I-34151 Trieste, Italy

[5] IITP RAS, Bolshoy Karetny Per 19,Build 1, Moscow 127051, Russia

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 413卷

关键词：

Differential graded algebra; Infinite jet bundle; Equation manifold; Massey products; A infinity-algebra; Formality; CONSERVATION-LAWS; CHARACTERISTIC COHOMOLOGY; VARIATIONAL BICOMPLEX; ADDITIONAL SYMMETRIES; ALGEBRA; SYSTEMS;

D O I：

10.1016/j.jde.2024.08.057

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We work within the framework of the variational bicomplex: we define Ate-algebra structures on horizontal and vertical cohomologies of (formally integrable) partial differential equations with the help of Merkulov's theorem. Since higher order Ate-algebra operations are related to Massey products, our observation implies the existence of invariants for differential equations that go beyond conservation laws. We also propose notions of formality for PDEs, and we present examples of formal equations. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：805 / 827

页数：23

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