Direct and inverse scattering on the line for one-dimensional Schrodinger equation

The direct and inverse scattering problems are studied for one-dimensional Schrodinger equation with a potential, which is asymptotically close to distinct periodic functions on the different half-axes, It is supposed that the background Hill operators have two bands spectra with the coinciding half-infinite band. It is also assumed that the perturbation has the second moment finite. For such a class of potentials the characterization of the scattering data is proposed and the inverse problem is solved.