Darboux transformations of the square of a Schrödinger operator and associated evolution equations Original Research Article

All operators which result from successive first-order Darboux transformations of the square of an arbitrary Schrödinger operator are determined. When the Schrödinger operatorʹs potential solves the KdV equation, ratios and wronskians of the (zero) eigenfunctions give the solutions of the evolution equations whose Lax operators are the Darboux transformed operators. This is illustrated by determining the rational solutions derived from the Adler-Moser class of KdV solutions.