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In this paper we consider supercritical nonlinear Schr\"odinger equations inan analytic Riemannian manifold $(M^d,g)$, where the metric $g$ is analytic.Using an analytic WKB method, we are able to construct an Ansatz for thesemiclassical equation for times independent of the small parameter. Theseapproximate solutions will help to show two different types of instabilities.The first is in the energy space, and the second is an immediate loss ofregularity in higher Sobolev norms.

Instabilities for supercritical Schr\"odinger equations in analytic manifolds