The dressing method as non linear superposition in sigma models

We apply the dressing method on Non Linear Sigma Model (NLSM), which describes propagation of strings $\mathbb{R}\times \mathrm{S}^2$, for an arbitrary seed. obtain a formal solution corresponding auxiliary system, is expressed in terms solutions NLSM that have same Pohlmeyer counterpart as Accordingly, we show can be applied without solving any differential equations. In this context superposition principle emerges: The dressed non-linear seed with