Differential equations over octonions

TL;DR

This paper explores solving differential equations over octonions using non-commutative line integration, addressing both linear and nonlinear cases, and discusses potential applications of these methods.

Contribution

It introduces methods for solving differential equations over octonions, expanding the mathematical toolkit for non-commutative algebraic structures.

Findings

Differential equations over octonions can be effectively solved.

Non-commutative line integration is a key technique used.

Applications in real-variable PDEs are outlined.

Abstract

Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is used. Such technique is applied to linear and non-linear partial differential equations in real variables. Possible areas of applications of these results are outlined.