Integration of vector hydrodynamical partial differential equations over octonions

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.

26 pages

References in corpus (4)

• Zeros of polynomials over Cayley-Dickson algebras
• Differentiable functions of Cayley-Dickson numbers
• Differential equations over octonions
• Line integration and second order partial differential equations over Cayley-Dickson algebras

Cited by in corpus (7)

• Unbounded normal operators in octonion Hilbert spaces and their spectra
• Metagroups and their smashed twisted wreath products
• Left invariant measures on locally compact fan loops
• Quasi-permutable normal operators in octonion Hilbert spaces and spectra
• On structure of topological metagroups
• Periodic integral operators over Cayley-Dickson algebras and spectra
• Homotopism of homological complexes over nonassociative algebras with metagroup relations