Non-Associative Structures and Their Applications in Differential Equations

Yakov Krasnov ()
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Yakov Krasnov: Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel

Mathematics, 2023, vol. 11, issue 8, 1-12

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.

Keywords: non-associative algebra; differential equations in algebra; Peirce decomposition; Kovalevskaya exponent (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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