Zakharov-Schulman system

From DispersiveWiki
Revision as of 06:10, 27 July 2006 by Tao (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigationJump to search

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 differneital 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].