The stability of full dimensional KAM tori for nonlinear Schrödinger equation

2017/12/21 by Hongzi Cong, Jianjun Liu, Yunfeng Shi +1 · 36 citations
Mathematics · Physics and Astronomy · #Geometry #Invariant (physics) #Kolmogorov–Arnold–Moser theorem #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear system #Numerical methods for differential equations #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Schrödinger equation #Stability (learning theory) #Torus

paper · doi:10.1016/j.jde.2017.12.013

published in Journal of Differential Equations 264(7), 4504-4563 (Elsevier BV)

openalex publication_date 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Citations

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

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• Long time stability for Lagrangian tori in infinite dimensional lattice systems
• On the existence of full dimensional KAM tori for 1D periodic nonlinear Schrödinger equation
• Invariant sets through resonant normal form for infinite dimensional holomorphic vector fields
• On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range
• The Existence of full dimensional tori for d-dimensional Nonlinear SchrOdinger equation
• The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation
• The Existence of Full-Dimensional KAM tori for one-dimensional nonlinear Klein-Gordon equation
• Analytic solutions of nonlinear elliptic equations on rectangular tori
• On the Stability of Periodic Multi-Solitons of the KdV Equation. [europepmc]