Title :
About structure of solutions of nonlinear synthesis problem of linear antenna according to the prescribed power directivity pattern
Author_Institution :
Inst. of Appl. Problems of Mech. & Math., Acad. of Sci., Lvov, Ukraine
Abstract :
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
Keywords :
antenna theory; bifurcation; directive antennas; functional equations; linear antennas; nonlinear equations; bifurcation; branching theory; excitation sources; linear antenna; mean-square deviation; nonlinear integrated equation solutions; nonlinear synthesis problem; power directivity pattern; real continuous functions; stabilizing functional; weighed restriction; Antenna theory; Artificial intelligence; Bifurcation; Differential equations; Electromagnetic fields; Mathematics; Nonlinear equations;
Conference_Titel :
Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, 2000. DIPED - 2000. Proceedings of the 5th International Seminar/Workshop on
Conference_Location :
Tbilisi
Print_ISBN :
966-02-1463-4
DOI :
10.1109/DIPED.2000.890005