J. d'Analyse Math. 115:1, 71-101 (2011) [DOI: 10.1007/s11854-011-0024-9]
On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data II. Perturbations with Finite Moments
Iryna Egorova and Gerald Teschl
We solve the Cauchy problem for the Korteweg-de Vries equation with steplike quasi-periodic, finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives with finite moments.