About structure of solutions of nonlinear synthesis problem of linear antenna according to the prescribed power directivity pattern

As an example of the synthesis problem of a linear antenna according to the prescribed power directivity pattern (DP), the results of research of the structure and properties of nonlinear integrated equation solutions, which is the Euler one of the goal functional, are presented. This functional includes both the requirement on the mean-square deviation, the given and synthesized DP by power, and the weighed restriction on the norm of the excitation sources in the form of the stabilizing functional. On the basis of the methods of branching theory of the nonlinear equations solutions it is shown that for the nonlinear synthesis problem the bifurcation of the solutions is characteristic. The equations for finding the bifurcation points are obtained. The quantity and characteristic properties difference from trivial solutions in the space of real continuous functions are determined.