Skyrme model on S-3 and harmonic maps

A nonlinear sigma model mimicking the Skyrme model on Sg is proposed and a family of classical solutions to the equations are constructed numerically. The solutions terminate into catastrophic-like spikes at critical values o f the Skyrme coupling constant and, when this constant is zero, they coinci de with the series of harmonic maps on Sg constructed some years ago by P. Bizon.