Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 13, pp. 1-10.

Title: Local well-posedness for a higher order nonlinear Schrodinger
       equation in Sobolev spaces of negative indices

Author: Xavier Carvajal (IMECC-UNICAMP, Campinas, Brazil)

Abstract: 
  We prove that the initial value problem associated with
  $$
  \partial_tu+i\alpha \partial^2_x u+\beta  \partial^3_x u
  +i\gamma|u|^2u  =  0, \quad x,t \in \mathbb{R},
  $$
  is locally well-posed in $H^s$ for $s>-1/4$. 

Submitted July 30, 2003. Published January 23, 2004.
Math Subject Classifications: 35Q58, 35Q60.
Key Words: Schrodinger equation; Korteweg-de Vries equation;
           trilinear estimate; Bourgain spaces.