2016/02/03 by Roberto Feola, Feola, Roberto
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Magnetic confinement fusion research #Numerical methods for differential equations #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1602.01341
openalex publication_date 2016/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove the existence of quasi-periodic, small-amplitude, solutions for quasi-linear Hamiltonian perturbations of the non-linear Schroedinger equation on the torus in presence of a quasi-periodic forcing. In particular we prove that such solutions are linearly stable. The proof is based on a Nash-Moser implicit function theorem and on a reducibility result on the linearized operator in a neighborhood of zero. The proof of the reducibility relies on changes of coordinates such as diffeomorphisms of the torus, pseudo-differential operators and a KAM-reducibility arguments. Due to the multiplicity of the eigenvalues we obtain a block-diagonalization.