modulation instability.

The method for controlling chaos in a ring resonator filled with a medium with cubic phase nonlinearity (Ikeda system), suggested in [1], is investigated within the framework of a distributed spatio-temporal model described by a Nonlinear Schr¨ odinger Equation with time-delayed boundary condition. Numerical results are presented which confirm the capability of the suggested method. For the case of weakly dispersive nonlinear medium, the results are in good agreement with the approximate theory based on the return map [1].

The paper describes results of experimental investigations on a formation of bright and dark envelope solitons with pulsed, monochromatic and two­frequency excitation of microwave spin waves in a magnetic film periodic structure – a magnonic crystal. The envelope solitons were excited at particular frequencies in the vicinity of magnonic bandgaps formed due to the Bragg resonance.