On the long-time asymptotics for the Korteweg–de Vries equation with steplike initial data associated with rarefaction waves

We discuss an asymptotical behavior of the rarefaction wave for the KdV equation in the region behind the wave front. The first and the second terms of the asymptotical expansion for such a solution with respect to large time were derived without detailed analysis in [1]. In the present work, we correct the formula for the second term by investigating the corresponding parametrix problem. We also study an influence of the resonance on the asymptotical behavior of the solution.