Abstract
We prove a Nekhoroshev type theorem for the nonlinear Schrödinger equation
where is a typical smooth Fourier multiplier and is analytic in both variables. More precisely, we prove that if the initial datum is analytic in a strip of width whose norm on this strip is equal to , then if is small enough, the solution of the nonlinear Schrödinger equation above remains analytic in a strip of width , with norm bounded on this strip by over a very long time interval of order , where is arbitrary and and are positive constants depending on and .
Citation
Erwan Faou. Benoît Grébert. "A Nekhoroshev-type theorem for the nonlinear Schrödinger equation on the torus." Anal. PDE 6 (6) 1243 - 1262, 2013. https://doi.org/10.2140/apde.2013.6.1243
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