A new criterion for the existence of KdV solitons in ferromagnets

The long-time evolution of the KdV-type solitons propagating in ferromagnetic materials is considered through a multi-time formalism, it is governed by all equations of the KdV hierarchy. The scaling coefficients of the higher order time variables are explicitly computed in terms of the physical parameters, showing that the KdV asymptotic is valid only when the angle between the propagation direction and the external magnetic field is large enough. The one-soliton solution of the KdV hierarchy is written down in terms of the physical parameters. A maximum value of the soliton parameter is determined, above which the perturbative approach is not valid. Below this value, the KdV soliton conserves its properties during an infinite propagation time.