A method to obtain a new class of discrete eigenfunctions and associated real, nonsingular, decaying, “reflectionless” potentials to the time dependent Schrödinger equation is presented. Using the inverse scattering transform, related solutions of the Kadomtsev-Petviashvili equation are found. The eigenfunctions have poles of order $m$, $m>\mathrm{}1\mathrm{}$ in the complex plane and are also characterized by an index, or “charge,” which is obtained as a constraint in the theory.

• Received 8 July 1996

DOI:https://doi.org/10.1103/PhysRevLett.78.570