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

Abstract

We prove that the Cauchy problem associated to the Zakharov-Schulman system $i{u}_t+L_{1}u=uv$, $L_{2}v=L_3(|u{|}^2)$ is locally well-posed for given initial data in Sobolev spaces $H^s(R^n)$, $s\ge n/4$, for n =2,3. Here, L_j denote second order operators, with L_1 non-degenerate and L_2 elliptic.

withdrawn