Potentials for solenoidal fields using the three-dimensional -harmonic cyclic algebra
Abstract
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 with respect to which the components of all the functions L are solutions, where 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 we get families of solutions for the Laplace equation with three independent variables.
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