  It is shown how a integrable mechanical system provides all the localized
static solutions of a deformation of the linear O(N)-sigma model in two
space-time dimensions. The proof is based on the Hamilton-Jacobi separability
of the mechanical analogue system that follows when time-independent field
configurations are being considered. In particular, we describe the properties
of the different kinds of kinks in such a way that a hierarchical structure of
solitary wave manifolds emerges for distinct N.
