The WKB method and geometric instability for non linear Schrödinger equations on surfaces

نویسنده

  • Laurent Thomann
چکیده

Let (M, g) be a Riemannian surface (i.e. a Riemannian manifold of dimension 2), orientable or not. We assume that M is either compact or a compact perturbation of the euclidian space, so that the Sobolev embeddings are true. Consider ∆ = ∆ g the Laplace-Beltrami operator. In this paper we are interested in constructing WKB approximations for the non linear cubic Schrödinger equation i∂ t u(t, x) + ∆u(t, x) = ε|u| 2 u(t, x), ε = ±1 u(0, x) = u 0 (x) ∈ H σ (M) (1.1)

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تاریخ انتشار 2006