Geometry of Chen–Lee–Liu type derivative nonlinear Schrödinger flow

In this paper we derive the Lie algebraic formulation of the Chen–Lee–Liu (CLL) type generalization of derivative nonlinear Schrödinger equation. We also explore its Lie algebraic connection to another derivative nonlinear Schrödinger equation, the Kaup–Newell system. Finally it is shown that the CLL equation is related to the Dodd–Caudrey–Gibbon equation after averaging over the carrier oscillation.