Solitons as nonlinear magnons

It is shown that the slowly varying nonlinear envelope of linear magnons satisfies the nonlinear Schr\"odinger equation. The derivation is based on the Landau-Lifshitz equation. The approximation shows that even weakly nonlinear effects, fully treated, yield types of excitations that cannot be adequately discussed by finite-order linear perturbation theory. This result is analogous to and was motivated by those of Krumhansl and Schrieffer.