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- Title
Non-Associative Structures and Their Applications in Differential Equations.
- Authors
Krasnov, Yakov
- Abstract
This article establishes a connection between nonlinear DEs and linear PDEs on the one hand, and non-associative algebra structures on the other. Such a connection simplifies the formulation of many results of DEs and the methods of their solution. The main link between these theories is the nonlinear spectral theory developed for algebra and homogeneous differential equations. A nonlinear spectral method is used to prove the existence of an algebraic first integral, interpretations of various phase zones, and the separatrices construction for ODEs. In algebra, the same methods exploit subalgebra construction and explain fusion rules. In conclusion, perturbation methods may also be interpreted for near-Jordan algebra construction.
- Subjects
DIFFERENTIAL equations; NONASSOCIATIVE algebras; NONLINEAR theories; DIFFERENTIAL algebra; ALGEBRA; SPECTRAL theory
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 8, p1790
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11081790