The putative classical soliton in the minimal nonlinear u model (no Skyrme term) is known to be unstable to collapse. We note that the imposition of a short-distance cutoff (which is anyway physically reasonable for a nonrenormalizable model) yields a stable classical soliton. We further suggest that this cutoff, carrying as it does some implicit dynamical information, be treated as a quantized dynamical variable. The resulting one-(experimentally fixed) parameter model agrees with experiment roughly as well as the simple a model with the Skyrme term. We interpret this feature as an indication of the robustness of the description of the nucleon as being dominated by a hedgehog-type meson cloud. It is suggested that the same approach might be useful in some other situations where the long-distance description of the physics is more precisely known than is the short-distance description.

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General methods in search of stable structures in (3 + 1)-dimensional models are presented. Using the Skyrme model as an example, we exhibit the methods and demonstrate their ability to pick out the minimal-energy configurations. In the class of fields with unit topological charge these are the well-known Skyrmions (the spherically symmetric configurations), which realize the absolute minimum of the energy. In the second and higher homotopy classes the minimal-energy configurations are, however, of the axisymmetric type. We argue that these methods provide a good guide and support to numerical analysis of multidimensional structures in essentially nonlinear models for liquid crystals, cosmology, ferromagnets, nonlinear elasticity, and so on.

Not widely known facts on the genesis of the Skyrme model are presented in a historical survey, based on Skyrme's earliest papers and on his own published remembrance. We consider the evolution of Skyrme's model description of nuclear matter from the "Mesonic Fluid" model up to its final version, known as the baryon model. We pay special tribute to some well-known ideas in contemporary particle physics which one can find in Skyrme's earlier papers, such as: Nuclear Democracy, the Solitonic Mechanism, the Nonlinear Realization of Chiral Symmetry, Topological Charges, Fermi–Bose Transmutations, etc. It is curious to note in the final version of the Skyrme model gleams of Kelvin's "Vortex Atoms" theory. In conclusion we make a brief analysis of the validity of Skyrme's conjectures in view of recent results and pinpoint some questions which still remain.