Solitons and nuclei

Skyrmions are topological soliton solutions that model nuclei. The soliton solutions are not tractable analytically and therefore need to be computed numerically by solving highly nonlinear partial differential equations in three-dimensional space. The numerical results reveal surprising and unexpected symmetries, including those of the Platonic solids. Using an approximate description in terms of rational maps between Riemann spheres leads to an understanding of these symmetries and an interesting energy minimization problem in the space of rational maps. The results are compared to experimental data on nuclei.