  We study long wave limits for general Schrodinger maps systems into Kahler
manifolds with a constraining potential vanishing on a Lagrangian submanifold.
We obtain KdV type systems set on the tangent space of the submanifold. Our
general theory is applied to study the long wave limit of the Gross-Pitaevskii
equation, and of the Landau-Lifshitz systems for ferromagnetic and
antiferromagnetic chains.
