Defocusing Nonlinear Schrr Odinger Equation: Connnement, Stability and Asymptotic Stability Keywords. Nonlinear Schrr Odinger Equation { Dispersion {pseudo-con- Formal Law { Time-dependent Rescalings { Stability { Large Time Asymp- Totics { Minimzers { Relative Entropy { Csiszz Ar-kullback Inequality
نویسنده
چکیده
This paper is devoted to the asymptotic properties of the Nonlinear Schrr odinger equation in the defocusing case. We recover dispersion rates by the mean of time-dependent rescalings in the power law case and prove a new result in the case of the logarithmic Nonlinear Schrr odinger equation. The rescaled equation is then used to obtain an asymptotic result of nonlinear stability, which is the main result of this paper.
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