Numerical and Analytical Investigations of Nonlinear Synthesis Problems of Antenna with the Flat Radiating Aperture

Abstract

The review article contains results of researches of the synthesis problems of radiating systems with incomplete input information arising in particular during optimal design of radio, acoustic or other types of radiating systems (RS) by the given requirements to energy characteristics of radiated field. In mathematical terms, these tasks are reduced to study and nume­rical solution of one class of two-dimensional nonlinear integral equations of Hammerstein type that depend on two real para­meters. It was established that a characteristic feature of this class of equations is nonuniqueness and the branching (or bifur­cation) of existing solutions. Methods of solving two-parametric nonlinear spectral problem, which is necessary to finding the set of points of branching are proposed. Algorithms and numerical methods for the finding of branching solutions are built and founded. Numerous examples of specific synthesis problems are presented.