  Soliton spheres are immersed 2-spheres in the conformal 4-sphere S^4=HP^1
that allow rational, conformal parametrizations f:CP^1->HP^1 obtained via
twistor projection and dualization from rational curves in CP^{2n+1}. Soliton
spheres can be characterized as the case of equality in the quaternionic
Pluecker estimate. A special class of soliton spheres introduced by Taimanov
are immersions into R^3 with rotationally symmetric Weierstrass potentials that
are related to solitons of the mKdV-equation via the ZS-AKNS linear problem. We
show that Willmore spheres and Bryant spheres with smooth ends are further
examples of soliton spheres. The possible values of the Willmore energy for
soliton spheres in the 3-sphere are proven to be W=4pi*d with d a positive
integer but not 2,3,5, or 7. The same quantization was previously known
individually for each of the three special classes of soliton spheres mentioned
above.
