The properties of solutions of the synthesis problem for the waveguide array

The synthesis problem of waveguide array with due regard for the mutual coupling of the elements is considered. The variational statement of problem consists in minimization of functional presenting the mean-square deviation of the prescribed and synthesized amplitude radiation patterns; the functional contains additional summand, which specifies limitation on a norm of the excitation coefficients of the array elements. The nonlinear equation, corresponding to a functional, is solved numerically by the method of successive approximations. The linear equation for investigation of branchpoints is obtained. The results of numerical calculations are discussed