KAM for quasi-linear autonomous NLS

2017/05/20 by Roberto Feola, Michela Procesi, Feola, Roberto +1 · 7 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Amplitude #Analysis of PDEs (math.AP) #Applied mathematics #Artificial intelligence #Class (philosophy) #Computer science #FOS: Mathematics #Hamiltonian system #Kolmogorov–Arnold–Moser theorem #Mathematical analysis #Mathematics #NLS #Nonlinear Photonic Systems #Nonlinear system #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Quasi periodic #Stability (learning theory) #math.AP

paper · pdf · doi:10.48550/arxiv.1705.07287

published in arXiv (Cornell University) (Cornell University)

arxiv created 2017/05/20 · openalex publication_date 2017/05/20 · arxiv updated 2017/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We consider a class of fully nonlinear Schrödinger equations and we prove the existence and the stability of Cantor families of quasi-periodic, small amplitude solutions. We deal with reversible autonomous nonlinearities and we look for analytic solutions. Note that this is the first result on analytic quasi-periodic solutions for fully nonlinear PDEs.

Citations

• Newton's method and periodic solutions of nonlinear wave equations
• Invariant Cantor Manifolds of Quasi-Periodic Oscillations for a Nonlinear Schrodinger Equation

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