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

aIt has been proposed to classify waves (oscillations), existing only when they connect with each other directly or through a source, as attached. In the first case, the waves are described by nonorthogonal (in the energy sense) solutions of homogeneous boundary value problems, which exist as a "product" of realization of the problem of complex wave excitation. In the second case, the waves are described by solutions of inhomogeneous boundary value problems on the adjoint Helmholtz equation, in the right-hand side of which there is a solution of the corresponding homogeneous boundary value problem. In both cases, the boundary value problems are self-consistent, since they form an inverse relationship between the waves through a source synchronized with these waves.