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 517.5 Given 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 A and a suitable affine vector field φ with respect to which the components of all functions L°φ are solutions, where L is differentiable in a sense of Lorch with respect to 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.