On The Cauchy Problem for the elliptic Zakharov-Schulman system in dimensions 2 and 3

Details On The Cauchy Problem for the elliptic Zakharov-Schulman system in dimensions 2 and 3 On The Cauchy Problem for the elliptic Zakharov-Schulman system in dimensions 2 and 3

2010-02-03

arxiv.org/abs/1002.0866v3

Mathematics

Analysis of PDEs

withdrawn

Scientific paper

We prove that the Cauchy problem associated to the Zakharov-Schulman system
$iu_t+L_1u=uv$, $L_2v=L_3(|u|^2)$ is locally well-posed for given initial data
in Sobolev spaces $H^s(R^n)$, $s\geq n/4$, for n =2,3. Here, L_j denote second
order operators, with L_1 non-degenerate and L_2 elliptic.

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