On a Class of Solutions to the Generalized Derivative Schrodinger Equations

In this work we shall consider the initial value problem associated to the generalized derivative Schr?dinger(gDNLS) equations ■ and ■ Following the argument introduced by Cazenave and Naumkin we shall establish the local well-posedness for a class of small data in an appropriate weighted Sobolev space. The other main tools in the proof include the homogeneous and inhomogeneous versions of the Kato smoothing effect for the linear Schr?dinger equation established by Kenig–Ponce–Vega.