T. Colin, C. Galusinski, and H. G. Kaper, "Waves in Ferromagnetic Media," Preprint ANL/MCS-P880-0301, March 2001. [pdf]
It is sown that small perturbations of equi8librium states in ferromagnetic media give rise to standing and traveling waves that are stable for long times. The evolution of the wave profiles is governed by semilinear heat equations. The mathematical model underlying these results consists of the Landau-Lifshitz equation for the magnetization vector and Maxwell's equations for the electromagnetic field variables. The model belongs to a general class of hyperbolic equations for vector-valued functions, whose asymptotic properties are analyzed rigorously. The results are illustrated with numerical examples.