Résumé
A yttrium-iron-garnet magnetic thin film, driven by means of two antennas, produces a standing wave in-plane magnetization. When the driving frequency is chosen close to the upper edge of the passing band, it is shown by rigorous asymptotic multiscale analysis that the governing model for the generated backward volume waves is the defocusing nonlinear Schrödinger equation. Although being driven inside the allowed band, the nonlinear response of the system is discovered to allow for the formation of bistable magnetization profiles for a film width comparable with the wavelength of the driving radiation.