Hyperbolic patterns

Hyperbolic patterns constructed basing on higher derivatives of the hyperbolic tangent represent specially designed sums of even powers of soliton-like excitations. Under certain limitations, the hyperbolic patterns satisfy solutions of an equation which is homomorphic to the Klein-Gordon one. Since the hyperbolic patterns may be considered as mathematical images of wave packets, the problem of de Broglie's double solution is discussed. The hyperbolic patterns can be used to construct spatially localized dynamic structures.