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About completeness of the systems of the boundary conditions of boundary value problems, solved in the unclosed form

Keywords:

V. A. Malakhov – Dr.Sc. (Eng.), Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev
E-mail: physics@nntu.ru
E. V. Pavlovich – Head of 1203 VP of RF DoD, FSUE FRPC “Measuring System Research Institute n.a. Yu.Ye. Sedakov”
A. A. Raevskaya – Post-graduate Student, Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev; Engineer, FSUE FRPC “Measuring System Research Institute n.a. Yu.Ye. Sedakov”


The question of significance of the completeness of the system of boundary conditions on the example of periodically irregular guide structures is considered, whose boundary-value problems are posed in the non-closed form.
The example of periodically irregular guide structures shows how an incorrect arrangement of boundary condition systems can lead to a change in the type of the electrodynamic operator, which entails the loss of some of the solutions (or the acquisition of false ones) of the boundary value problem, that is, to an incorrect representation of the spectrum of the waves of the guiding structure.
It is shown that the complex waves of a circular diaphragm waveguide have the properties common to CW: the dispersion characteristics of the CW start at the two-digit sections of the dispersion characteristics of propagating waves at points where the group velocity vanishes and ends at the upper boundary of the region of reactive attenuation of normal waves.

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May 29, 2020

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