Vol. 14, No. 8, 2021

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Quasiperiodic solutions of NLS with Liouvillean frequencies

Xindong Xu, Jiangong You and Qi Zhou

Vol. 14 (2021), No. 8, 2327–2362
Abstract

We prove the existence of time quasiperiodic solutions with Liouvillean frequencies for the forced nonlinear Schrödinger equation (NLS). The tool utilized here is a new infinite-dimensional KAM theorem that applies to Liouvillean frequencies.

Keywords
Liouvillean frequency, quasiperiodic solution, KAM
Mathematical Subject Classification 2010
Primary: 37K55
Secondary: 35Q55
Milestones
Received: 11 July 2018
Revised: 14 May 2020
Accepted: 27 August 2020
Published: 19 December 2021
Authors
Xindong Xu
School of Mathematics
Southeast University
Nanjing
China
Jiangong You
Chern Institute of Mathematics and LPMC
Nankai University
Tianjin
China
Qi Zhou
Chern Institute of Mathematics and LPMC
Nankai University
Tianjin
China