# Zakharov-Schulman system

The Zakharov-Schulman system is described by the equations

${\displaystyle iu_{t}+L_{1}u=\phi u}$
${\displaystyle L_{2}\phi =L_{3}(|u|^{2})}$

where L_1, L_2, L_3 are various constant coefficient differential operators; these describe the interactions of small amplitude, high frequency waves with acoustic waves ZkShl1980. Using energy methods and gauge transformations, local existence for smooth data was established in KnPoVe1995b; see also GhSau1992.

The Davey-Stewartson system can be viewed as a special case of this system.