I. A. Vdovichenko - Ph.D. (Phys.-Math.), Associate Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev E-mail: physics@nntu.nnov.ru 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; Honored Scientist of RF S. B. Raevskij - Dr.Sc. (Eng.), Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev; Honored Scientist of RF

The boundary self-consistent problems which describe oscillations and waves, connected to the source have been formulated. The formulated problems are taken into account the effect of the reverse field on the source, since the wave numbers both in the field functions, and in the source functions are the same. The amplitudes of these waves and oscillations depend on the longitudinal coor-dinate. The oscillations and waves are adjoint because they are described by the attached Helmholtz equations, the right part of which are the solutions of the corresponding homogeneous boundary value problems. Formed in such a way boundary problems should be called self-consistent. The waves (oscillations), described by such problems are \"tied\" to the source, have the opposite effect on it and exist only if there is the source. In this sense, they can not be called its own. The article prompted to call them attached to the source. The article sets out the conditions of existence of solutions of semi-homogeneous boundary value problems corresponding to the im-proper waves. The boundary conditions of the boundary value problem are executed in the case when the system of homogeneous and heterogeneous linear algebraic equations have joint solutions. The system of homogeneous equations has nontrivial solutions only if its determinant is equal to zero. Since the main determinant of the system of inhomogeneous equations coincides with the determinant of the system of homogeneous equations, a system of non-homogeneous equations can have solutions only when its additional de-terminants are equal to zero.

 

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