ON THE EXISTENCE OF FULL DIMENSIONAL KAM TORUS FOR FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION

DOI10.11948/20190292zbMath1455.37061OpenAlexW3003407063MaRDI QIDQ4964048

Yuan Wu, Xiao Ping Yuan

Publication date: 24 February 2021

Published in: Journal of Applied Analysis & Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11948/20190292

zbMATH Keywords

KAM theoryalmost periodic solutionfractional nonlinear Schrödinger equationGevrey space

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Fractional partial differential equations (35R11)

Related Items

Kolmogorov-Arnold-Moser theorem for nonlinear beam equations with almost-periodic forcing

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• KAM for autonomous quasi-linear perturbations of mKdV
• Nonlinear fractional Schrödinger equations in one dimension
• A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations
• Invariant tori of full dimension for a nonlinear Schrödinger equation
• The stability of full dimensional KAM tori for nonlinear Schrödinger equation
• Small divisors with spatial structure in infinite dimensional Hamiltonian systems
• KAM for the nonlinear Schrödinger equation
• Localization in disordered, nonlinear dynamical systems
• Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
• Nearly integrable infinite-dimensional Hamiltonian systems
• Quasi-periodic solutions for fractional nonlinear Schrödinger equation
• Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
• Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations
• An abstract Birkhoff normal form theorem and exponential type stability of the 1d NLS
• On the existence of full dimensional KAM torus for nonlinear Schrödinger equation
• Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations
• Almost periodic solutions of one dimensional Schrödinger equation with the external parameters
• On invariant tori of full dimension for 1D periodic NLS
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• Newton's method and periodic solutions of nonlinear wave equations
• Quasi-periodic solutions of a fractional nonlinear Schrödinger equation
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
• On the construction of almost periodic solutions for a nonlinear Schrödinger equation
• Almost periodic solutions for a class of higher-dimensional beam equations
• An integrable normal form for water waves in infinite depth