  The detailed analysis of the generalised Weierstrass representation of
surfaces of revolution and their deformations induced by the modified
Korteweg--de Vries (mKdV) equations is done. In particular, it is shown that
these deformations preserve tori. The geometric meaning of the potential of
surface is discussed and the deformations of potentials induced by geometric
deformations (the Moebius inversion and a passing to a dual surface) are
described. The conjecture of invariance of first integrals of the mKdV
hierarchy, considering as invariants of surfaces, with respect to confomal
changes of the metric of the ambient space is introduced. Some numeric
computations confirming it are also presented. This paper is the sequel to the
previous author's paper "Modified Novikov-Veselov equation and differential
geometry of surfaces" (dg-ga/9511005) where generic surfaces are considered.
Here the surfaces of revolution are regarded as a toy model for the general
case.

Differential Geometry;Differential Geometry