Reflectionless approximations to potentials with band structure

Inverse scattering methods are used to construct approximations to one-dimensional periodic potentials with a known band structure. By nature of the construction, these potentials give rise to reflectionless continuum scattering. A partial differential equation describing the problem and a numerical method for its solution are given. Some simple examples illustrate the degree to which the approximations correctly represent known potentials. Possible applications of the authors methods are noted