A Large Time Asymptotics for Transparent Potentials for the Novikov–Veselov Equation at Positive Energy

Abstract

In the present paper we begin studies on the large time asymptotic behavior for solutions of the Cauchy problem for the Novikov-Veselov equation (an analog of KdV in 2 + 1 dimensions) at positive energy.In addition, we are focused on a family of reflectionless (transparent) potentials parameterized by a function of two variables.In particular, we show that there are no isolated soliton type waves in the large time asymptotics for these solutions in contrast with well-known large time asymptotics for solutions of the KdV equation with reflectionless initial data.