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Self-consistent waveguide boundary value problems as problems on oscillations and waves attached to a source


A. S. Raevskij – Dr.Sc. (Phys.-Math.), Professor, Head of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev
S. B. Raevskij – Honored Scientist of RF, Dr.Sc. (Eng.), Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev
A. Yu. Sedakov – Dr.Sc. (Eng.), Professor of Department of Physics and Technology of Optical Communication,
Nizhny Novgorod State Technical University n.a. R.E. Alekseev; Director of FRPC “Measuring System Research Institute n.a. Yu.Ye. Sedakov” (Nizhny Novgorod)

Self-consistent boundary-value problem in any production are the objectives for the eigenfunctions and eigenvalues of, i.e., lead to either the homogeneous integral equations (systems of equations), or are formulated on the equations of Helmholtz type with the right part, which is the solution of the homogeneous boundary value problem for this equation. This equation can be called an attached Helmholtz equation. Solving such problems is presented in closed form, so we can talk about the selective excitation of waves (oscillations) in the guide (oscillatory) structure. Because the waves (oscillations) are somehow related to the source, it is not necessary to call its own, and it is expedient to classify as attached to the source, because they do not exist in the absence of the latter. Such are the complex wave (CW), forming a complex resonance (CR), these are CW, excited by an independent source-type antenna of the traveling wave. In the present work the solution of self-consistent problem are regarded as describing vibrations and waves, attached to the source, selectively excited by the latter. Such waves (oscillations) should be regarded as improper.
A complex resonance in inhomogeneous guiding structures that differ from the normal resonance of its existence not at the point in the whole range of existence of CW, occurs only in the presence of source through which are looped forward and reverse power flows. Thus, the two interacting CW are "attached" to the source, and the CR is "attached" to the source of electromagnetic oscillation, which, due to the mandatory presence of the source is not own. CR corresponds to the oscillation field is formed, localized near the origin, i.e. having the form of a standing wave with amplitude decreasing exponentially with distance from the source in accordance with the longitudinal dependence of the field CW. This oscillation corresponds to the boundary value problem for the adjoint Helmholtz equation with a lower source function in the right part. The problem of excitation of CR is self-consistent source generates a few CW that form closed using a power. It refers to the first version attached above boundary value problem. As a private, CW individually excited distributed source of a traveling wave.
The term "waves (oscillations) that are attached to the source" was introduced with the aim to bring the mathematical concept of "adjoint solution" to his physical (in this particular situation) sense. The adjoint solution associated with the problem of excitation, should not be regarded as private.

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