For the defocusing nonlinear Schrö dinger equation on the circle, we construct a Birkhoff map Φ which is tame majorant analytic in a neighborhood of the origin. Roughly speaking, majorant analytic means that replacing the coefficients of the Taylor expansion of Φ by their absolute values gives rise to a series (the majorant map) which is uniformly and absolutely convergent, at least in a small neighborhood. Tame majorant analytic means that the majorant map of Φ fulfills tame estimates. The proof is based on a new tame version of the Kuksin-Perelman theorem (2010 Discrete Contin. Dyn. Syst. 1 1-24), which is an infinite dimensional Vey type theorem.
|Titolo:||Tame majorant analyticity for the Birkhoff map of the defocusing nonlinear Schrödinger equation on the circle|
|Data di pubblicazione:||2018|
|Digital Object Identifier (DOI):||10.1088/1361-6544/aaa7ba|
|Appare nelle tipologie:||1.1 Journal article|