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 .

We describe the kink solitary waves of a massive nonlinear sigma model with an S2 sphere as the target manifold. Our solutions form a moduli space of nonrelativistic solitary waves in the long wavelength limit of ferromagnetic linear spin chains.

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In this paper we describe the moduli space of kinks in a class of systems of two coupled real scalar fields in (1+1) Minkowskian space-time. The main feature of the class is the spontaneous breaking of a discrete symmetry of (real) Ginzburg-Landau type that guarantees the existence of kink topological defects.

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