SOLUTIONS OF A DERIVATIVE NONLINEAR SCHRÖDINGER HIERARCHY AND ITS SIMILARITY REDUCTION

Abstract

The hierarchy structure of a derivative nonlinear Schrödinger equation is investigated in terms of the Sato-Segal-Wilson formulation. Special solutions are constructed as ratios of Wronski determinants. Relations to the Painlevé IV and the discrete Painlevé I are discussed by applying a similarity reduction.