A semi-periodic initial-value problem for the Kadomtsev–Petviashvili II equation

We investigate the Cauchy problem on the cylinder, namely the semi-periodic problem where there is periodicity in the x-direction and decay in the y-direction, for the Kadomtsev–Petviashvili II equation by the inverse spectral transform method. For initial data with small L 1 and L 2 norms, assuming the zero mass constraint, this initial-value problem is reduced to a Riemann–Hilbert problem on the boundary of certain infinite strips with shift.