Potentials for solenoidal fields using the three-dimensional $φ$-harmonic cyclic algebra
Given a PDE in [10] it is proposed a method for constructing solutions by considering an associative real algebra A, and a suitable affine vector field $φ$ with respect to which the components of all the functions $\mathcal{L}\circφ$ are solutions, where $\mathcal L$ is differentiable in the sense of Lorch with respect to A. When we consider the 3D cyclic algebra and a suitable 3D affine map $φ$ we get families of solutions for the Laplace equation with three independent variables.
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