Spectrum of magnetostatic waves in a ferromagnet with a moving superlattice of domain walls

The spectral properties of magnetostatic waves in a ferromagnet with a moving periodic domain structure are considered within the exchange-free magnetostatic approximation. It is demonstrated that the Doppler frequency shift caused by the domain-wall motion leads to the splitting of the spectrum of each magnetostatic wave mode into two dispersion branches, namely, into high-frequency and low-frequency branches. It is established that the larger the mode number, the larger the separation between these branches with respect to the mode spectrum in the presence of the static domain structure.