  The Novikov-Veselov (NV) equation is a
  (2+1)-dimensional nonlinear evolution equation that generalizes the
  (1+1)-dimensional Korteweg-deVries (KdV) equation. Solution of the NV
equation using the inverse scattering method has been discussed in the
literature, but only formally (or with smallness assumptions in case of nonzero
energy) because of the possibility of exceptional points, or singularities in
the scattering data. In this work, absence of exceptional points is proved at
zero energy for evolutions with compactly supported, smooth and rotationally
symmetric initial data of the conductivity type:
$q_0=\gamma^{-1/2}\Delta\gamma^{1/2}$ with a strictly positive function
$\gamma$. The inverse scattering evolution is shown to be well-defined,
real-valued, and preserving conductivity-type. There is no smallness assumption
on the initial data.
