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DOI: 10.23952/jnfa.2022.12
Received October 9, 2021; Accepted March 7, 2022; Published April 5, 2022
Abstract This paper focuses on the quintic Schrödinger equation with quasi-periodic forcing on the two dimensional torus under periodic boundary conditions. By utilizing the measure estimation of infinitely many small divisors, for most values of the frequency vectors, the Hamiltonian of the linear part of the equation can be reduced to an autonomous system by a symplectic change of coordinates. By some transformations of coordinates, the Hamiltonian of the equation can be transformed into an angle-dependent block-diagonal normal form, which can be achieved by choosing the appropriate tangential sites. By an abstract KAM theorem, it is proved that the existence of a class of invariant tori implies the existence of a class of small-amplitude quasi-periodic solutions to the equation.
How to Cite this Article:
M. Zhang, X. Wang, Z. Hu, Invariant tori for the quintic Schrödinger equation with quasi-periodic forcing on the two-dimensional torus under periodic boundary conditions, J. Nonlinear Funct. Anal. 2022 (2022) 12.