On instability for the cubic nonlinear Schrodinger equation
نویسندگان
چکیده
We study the flow map associated to the cubic Schrödinger equation in space dimension at least three. We consider initial data of arbitrary size in Hs, where 0 < s < sc, sc the critical index, and perturbations in Hσ , where σ < sc is independent of s. We show an instability mechanism in some Sobolev spaces of order smaller than s. The analysis relies on two features of super-critical geometric optics: creation of oscillation, and ghost effect.
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