  A class of "elliptic soliton" solutions of the Kadomtsev-Petviashvili
hierarchy, which includes a determinantal solution of Li and Zhang, is
described in terms of pseudo-differential operator formulation. In our
approach, the Li-Zhang solution is obtained by repeatedly applying the Darboux
transformation to a stationary solution. Real-valued solutions are discussed
and various examples that display web-like patterns are presented.
