Non-Associative Structures and Their Applications in Differential Equations

Yakov Krasnov

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Article number1790
JournalMathematics
Volume11
Issue number8
DOIs
StatePublished - Apr 2023

Bibliographical note

Publisher Copyright:
© 2023 by the author.

Keywords

  • Kovalevskaya exponent
  • Peirce decomposition
  • differential equations in algebra
  • non-associative algebra

Fingerprint

Dive into the research topics of 'Non-Associative Structures and Their Applications in Differential Equations'. Together they form a unique fingerprint.

Cite this