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By analogy to the theory of harmonic fields on the complex plane, we buildthe theory of wave-like fields on the plane of double variable. We constructthe hyperbolic analogues of point vortices, sources, vortice-sources and theirhigher-order multipole generalizations. We examine the physical aspects and thepossibility of extension to the space of polynumbers of higher dimensions.

The hyperbolic field theory on the plane of double variable