Skyrme model

The Skyrme model is a nonlinear sigma model for an $SU(2)$-valued field supplemented by a four-derivative term that evades Derrick collapse. Its topological degree is baryon number, and finite-energy solitons are Skyrmions.

A Skyrmion is a finite-energy topological soliton of the Skyrme model. Its baryon number is the degree of the compactified spatial map $S^3\to SU(2)\simeq S^3$.

The rational map approximation writes the angular dependence of a Skyrmion using a rational map $R:S^2\to S^2$ and determines a radial profile variationally. The degree of $R$ equals the baryon number, while zeros of its Wronskian mark directions of vanishing angular baryon density.