Rigorous derivation of the NLS in magnetic films

The nonlinear Schrödinger (NLS) equation that gives an account of 'temporal' envelope soliton propagation in magnetic thin films is derived, using the rigorous asymptotic method of multiscale expansions. Magnetostatic backward volume waves are considered and inhomogeneous exchange is neglected. New mathematical features concerning multiscale expansions are found: both a propagating second harmonic term and the usual non-propagating one arise. The secular-type terms that arise in the transverse direction are no longer forbidden. The dispersion coefficient of the obtained NLS equation is not equal to the so-called group velocity dispersion, despite being a general law in bulk media. The nonlinear coefficient is in quite good agreement with the result of previous computations for physically relevant values of the parameters.