On the Zakharov and Zakharov-Schulman Systems

We consider the initial value problem for the Zakharov system [formula] 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 λ (the ionic speed of sound) in appropriate Sobolev spaces. The method provides similar results for the IVP for the Zakharov-Schulman system [formula] where u: Rd×[0, ∞)→ C, φ: Rd× [0, ∞)→ R, and [formula] with a(i,j)(k)=aki, j real constants, which models the interactions of small amplitude high frequency waves with acoustic type waves.