Nonlinear transverse standing spin wave modes of a magnetic film

We derive an asymptotic model for wave propagation across a ferromagnetic film, neglecting anisotropy and damping, close to the ferromagnetic resonance. The resulting model is a nonlinear Schrödinger equation, which can be either focusing or defocussing, depending on the magnitude and direction of the external magnetic field. We use it to compute the nonlinear eigenmodes of standing spin waves, that can be excited in the film; the eigenmodes can be expressed using Jacobi's elliptic functions. It is shown that their frequency spectrum varies with the amplitude of the modes.