Finite-gap solutions of the modified Novikov-Veselov equations: their   spectral properties and applications
  We construct finite-gap solutions to the modified Novikov-Veselov equations, describe their spectral properties and the reduction to the modified Korteweg--de Vries equation and explain its relation to soliton deformations of tori and the Willmore conjecture. 
I.A. Taimanov