Synthesis of Radiating Systems with Flat Aperture According to a Given Power Directivity Pattern. ІІ. Finding Solutions at the Bifurcation Points
- 18 Downloads
We continue our investigation of the problem of synthesis for a radiating system with flat aperture according to a prescribed power directivity pattern originated in [P. O. Savenko, J. Math. Sci., 208, No. 3, 366–381 (2015)]. As a characteristic feature of problems from this class, we can mention the non-uniqueness and bifurcations of their solutions. On the basis of the theory of branching, we present a technique of finding the nonzero solutions (in the first approximation). This technique enables us to determine the main properties of solutions, which significantly simplifies the problem of finding the optimal solutions of the problem of synthesis by numerical methods.
KeywordsBifurcation Point Amplitude Distribution Radiate System Bifurcation Equation Newton Diagram
Unable to display preview. Download preview PDF.
- 1.M. M. Vainberg and V. A. Trenogin, Theory of Branching of the Solutions of Nonlinear Equations [in Russian], Nauka, Moscow (1969).Google Scholar
- 2.P. P. Zabreiko, A. I. Koshelev, M. A. Krasnosel’skii, et al., Integral Equations [in Russian], Nauka, Moscow (1968).Google Scholar
- 3.L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian[, Nauka, Moscow (1977).Google Scholar
- 4.M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, et al., Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).Google Scholar
- 6.P. A. Savenko and L. P. Protsakh, “Implicit function method in solving the nonlinear two-dimensional spectral problem,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 11(546), 41–44 (2007).Google Scholar
- 7.P. O. Savenko, Nonlinear Problems of Synthesis of Radiating Systems (Theory and Methods of Solution) [in Ukrainian], Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv (2002).Google Scholar
- 8.P. O. Savenko, “Synthesis of radiating systems with flat aperture according to a prescribed power directivity pattern. I. Finding the set of bifurcation points of the solutions,” Mat. Met. Fiz.-Mekh. Polya, 56, No. 4, 83–95 (2013); English translation: J. Math. Sci., 208, No. 3, 366–381 (2015).Google Scholar
- 9.P. O. Savenko, “A numerical algorithm for solving the generalized eigenvalue problem for completely continuous self-adjoint operators with nonlinear spectral parameter,” Mat. Met. Fiz.-Mekh. Polya, 40, No. 1, 146–150 (1997); English translation: J. Math. Sci., 88, No. 3, 452–455 (1998).Google Scholar
- 10.P. O. Savenko and L. P. Protsakh, “Variational approach to the solution of the nonlinear vector spectral problem for the case of self-adjoint positive semidefinite operators,” Dop. Nats. Akad. Nauk Ukr., No. 6, 26–31 (2004).Google Scholar