  We use the inverse scattering method to construct classical solutions for the
Novikov-Veselov (NV) equation, solving a problem posed by Lassas, Mueller,
Siltanen, and Stahel. We exploit Bogadanov's Miura-type map which transforms
solutions of the modified Novikov-Veselov (mNV) equation into solutions of the
NV equation. We show that the Cauchy data of conductivity type considered by
Lassas, Mueller, Siltanen, and Stahel correspond precisely to the range of the
Miura map, so that it suffices to study the mNV equation. We solve the mNV
equation using the scattering transform associated to the defocussing
Davey-Stewartson II equation.
