Integration of vector hydrodynamical partial differential equations over octonions

TL;DR

This paper introduces a novel integration technique for specific vector partial differential equations using non-commutative integration over Cayley-Dickson algebras, with applications to fluid flow models.

Contribution

It develops a new method for integrating certain PDEs via non-commutative calculus over Cayley-Dickson algebras, expanding analytical tools for complex vector equations.

Findings

Successfully applied to Korteweg-de-Vries and Kadomtzev-Petviashvili equations

Provides solutions for non-isothermal flows of incompressible liquids

Demonstrates the effectiveness of non-commutative integration methods

Abstract

New technique of integration of certain types of partial differential equations is developed. For this purpose non-commutative integration over Cayley-Dickson algebras is used. Applications to non-linear vector partial differential equations of Korteweg-de-Vries and Kadomtzev-Petviashvili types and describing non-isothermal flows of incompressible Newtonian liquids are given.