Electron. J. Diff. Eqns., Vol. 2004(2004), No. 13, pp. 1-10.

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

Xavier Carvajal

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 $s$ greater than $-1/4$.

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.

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Xavier Carvajal
Caixa Postal: 6065
13083-859, Barao Geraldo
Campinas, SP, Brazil
email: carvajal@ime.unicamp.br

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