Helmholtz equations of electromagnetic waves in hyperbolic the magnetized gyrotropic elliptic wave guides

The generalized equations of Helmholtz of electromagnetic waves in the regular wave guides with orthogonal forms of a transverse section filled with the magnetized ferrite (the gyrotropic environment) are received. One of two cases of cross magnetization of ferrite when the direction distribution of electromagnetic wave and the direction of the outside magnetizing constant magnetic field are perpendicular is considered, namely - normal magnetization. A mathematical basis is the modified method of invariant conversions allowing to realize easily transition to any regular wave guide with the rectilinear and curvilinear orthogonal form of a transverse section: rectangular, round, elliptic. On the basis of the received expressions Helmholtz equations for the least probed gyrotropic elliptic wave guides for the first time are removed in case of normal (hyperbolic) magnetization. The provided Helmholtz equations allow to deliver and solve a boundary value problem of an elliptic wave guide in case of hyperbolic magnetization with further receiving the dispersing equation.