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

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 $s$ 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
IMECC-UNICAMP
Caixa Postal: 6065
13083-859, Barao Geraldo
Campinas, SP, Brazil
email: carvajal@ime.unicamp.br

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