Periodic Solutions to One-Dimensional Wave Equation with Piece-Wise Constant Coefficients

This work is concerned with analysis and optimization in coefficients of the 1−D,T-periodic wave equation with piece-wise constant coefficients inx. ForT-rational, the system is in resonant case (i.e., the corresponding homogeneous problem has nontrivial solutions [free oscillations or breathers]). The case ofT-irrational remains an outstanding open problem.