Adiabatic limit of the zakharov-rubenchik equation

The Zakharov-Rubenchik system appears in the context of Alfvén waves propagating in a magnetized plasma. This system “contains” the well-known Zakharov equation and the Benney equation for the interaction of high and low frequency waves. We prove the pointwise convergence of the magnetic field B to a solution of the nonlinear Schrödinger equation, in the adiabatic limit ∈ → 0.