Zakharov-Schulman system

The Zakharov-Schulman system is described by the equations

i u_t + L_1 u = phi u

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].