It is known that the KdV equation appears naturally in the geometry of the orientation preserving diffeomorphic group Diff(S 1 ). It is a geodesic flow of a L 2 metric on the Bott-Virasoro group. The nonlinear Schrodinger equation (NLSE) is an evolution equation analogous to the KdV equation which describes an isospectral deformation of the first order 2 x 2 matrix differential operator, yet the family of NSLE has not been studied via diffeomorphic groups. In this paper we derive the Kaup-Newell equation and its generalizations are the Euler-Poincare flows on the space of first-order scalar (or matrix) differential operators. We show that the operators involved in the flow generated by the action of Vect(S 1 ) are neither Poisson nor skew symmetric. We also discuss the relation between the KdV flow and the Kaup-Newell flow.