Stationary wave map ($\Delta Q+|\nabla Q{|}^{2}Q=0$)

A time-independent wave map is a harmonic map of its spatial domain into the target. For target $S^2$, its equation is $\Delta Q+|\nabla Q{|}^{2}Q=0$. In two dimensions inverse stereographic projection gives a smooth nonconstant example of finite wave map energy $4\pi$.