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.