Potentials for solenoidal fields using the three-dimensional $φ$-harmonic cyclic algebra - Díaz-Marín, Homero G.; López-González, Elifalet; Osuna, Osvaldo (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.5Given a PDE, in [E. López-González, E. A. Martínez-García, R.~Torres-Córdoba, Chaos, Solitons and Fractals, 73, Article 113757 (2023)], the authors proposed a method for the construction of solutions by considering an associative real algebra $\mathbb A$ and a suitable affine vector field $φ$ with respect to which the components of all functions $\mathcal L°φ$ are solutions, where $\mathcal L$ is differentiable in a sense of Lorch with respect to $\mathbb A.$ If we consider the 3D cyclic algebra and a suitable 3D affine map $φ,$ then we get families of solutions for the Laplace equation with three independent variables.