  In this paper we consider a Schrodinger equation on the circle with a
quadratic nonlinearity. Thanks to an explicit computation of the first Picard
iterate, we give a precision on the dynamic of the solution, whose existence
was proved by C. E. Kenig, G. Ponce and L. Vega. We also show that the equation
is well-posed in a space based on Lp norms in frequencies.
