Examples of static localized solutions of nonlinear equations in 3 + 1 dimensions. II - asymptotic analysis -

A scaling operator conserved by self-interacting nonlinear system, is introduced. Solutions of nonlinear equations, introduced in a previous article, are analysed with respect to their scaling properties. As a result, the solutions can be classified into two categories according to whether they are invariant for scaling or not. The ones which are not invariant for scaling are perturbative solutions. The other class of solutions are characteristic functions of the scaling operator with vanishing characteristic value and are non-perturbative. These are isolated solutions suitable for describing elementary particles