ON THE ZAKHAROV AND ZAKHAROV-SCHULMAN SYSTEMS

We consider the initial value problem for the Zakharov system [GRAPHICS] which models the long wave Langmuir turbulence in a plasma. Using the standard iteration scheme in the original system it is shown that the system is locally well-posed uniformly on lambda (the ionic speed of sound) in appropriate Sobolev spaces. The method provides similar results for the IVP for the Zakharov-Schulman system [GRAPHICS] where u: R(d)x[0, infinity)-->C, phi: R(d)x[0, infinity)-->R, and [GRAPHICS] with a(i,j)(k)=a(j,i)(k) real constants, which models the interactions of small amplitude high frequency waves with acoustic type waves. (C) 1995 Academic Press, Inc.