A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data

Abstract. In the present paper we are concerned with the Novikov–Veselov equation at negative energy, i.e. with the (2+1)–dimensional analog of the KdV equation integrable by the method of inverse scattering for the two–dimensional Schrödinger equation at negative energy. We show that the solution of the Cauchy problem for this equation with non–singular scattering data behaves asymptotically as const t3/4 in the uniform norm at large times t. We also prove that this asymptotics is optimal.