Branching of Solutions of the Nonlinear Equations Appearing in the Problems of Synthesis of Plane Antenna Arrays.

In the process of solving the problems of synthesis of antennas with given amplitude characteristics, it is often necessary to apply nonlinear spectral theory. The practical statement of the problems of synthesis is based on the use of the amplitudes of desired functions. A standard procedure of optimization is to deduce the Euler equation for the functional used as an optimization criterion. As a rule, the indicated equation is integral and nonlinear due to the specific features of the problem. This equation is characterized by the nonuniqueness of solutions and their branching or bifurcations. Finding branched solutions requires the investigation of the corresponding homogeneous equations and the corresponding eigenvalue problem. The analysis of the problem makes it possible to determine the set of points of the input parameters at which the corresponding eigenvalues are equal to one, which determines the points of branching of the solutions. These calculations demonstrate the ability of the proposed approach to numerically determine the solutions of nonlinear equations, their properties, and branching points of the solutions with relatively low computational costs. [ABSTRACT FROM AUTHOR]