A Nekhoroshev type theorem for the nonlinear Schrödinger equation on the d-dimensional torus
نویسنده
چکیده
Abstract We prove a Nekhoroshev type theorem for the nonlinear Schrödinger equation iut = −∆u+ V ⋆ u+ ∂ūg(u, ū) , x ∈ T, where V is a typical smooth potential and g is analytic in both variables. More precisely we prove that if the initial datum is analytic in a strip of width ρ > 0 with a bound on this strip equals to ε then, if ε is small enough, the solution of the nonlinear Schrödinger equation above remains analytic in a strip of width ρ/2 and bounded on this strip by Cε during very long time of order ε−α| ln ε| β for some constants C > 0, α > 0 and β < 1. MSC numbers: 37K55, 35B40, 35Q55.
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