A Jordan algebra approach to the cubic eiconal equation

TL;DR

This paper introduces a novel mathematical framework linking cubic solutions of the eiconal equation to cubic Jordan algebras, providing a new perspective for understanding these equations.

Contribution

It establishes a natural correspondence between cubic solutions of the eiconal equation and cubic Jordan algebras, revealing a new structural connection.

Findings

Identifies a correspondence between cubic solutions and Jordan algebras

Classifies solutions via isomorphism classes of Jordan algebras

Provides a new algebraic approach to the eiconal equation

Abstract

We establish a natural correspondence between (the equivalence classes of) cubic solutions of an eiconal type equation and (the isomorphy classes of) cubic Jordan algebras.