Normal form for the fractional nonlinear Schrödinger equation with cubic nonlinearity

DOI10.1007/s12346-023-00797-wzbMath1518.37075OpenAlexW4368370716MaRDI QIDQ6159613

Xindong Xu, Fuzheng Ma

Publication date: 8 May 2023

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-023-00797-w

zbMATH Keywords

KAM toridense normal frequency

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Fractional derivatives and integrals (26A33) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Fractional partial differential equations (35R11)

Cites Work

• Unnamed Item
• Energy supercritical nonlinear Schrödinger equations: quasiperiodic solutions
• Mapping properties of normal forms transformations for water waves
• Nonlinear fractional Schrödinger equations in one dimension
• A KAM algorithm for the resonant non-linear Schrödinger equation
• An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation
• KAM for the nonlinear beam equation
• A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces
• Quasi-periodic solutions of completely resonant nonlinear wave equations
• Quasi-periodic solutions for 1D Schrödinger equation with the nonlinearity \(|u|^{2p}u\)
• KAM for the nonlinear Schrödinger equation
• KAM tori for higher dimensional beam equation with a fixed constant potential
• Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
• Fractional quantum mechanics and Lévy path integrals
• Quasi-periodic solutions for fractional nonlinear Schrödinger equation
• A KAM theorem for one dimensional Schrödinger equation with periodic boundary conditions
• Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
• Quasi-periodic solutions for a nonlinear wave equation
• Time quasi-periodic gravity water waves in finite depth
• Fractional nonlinear Schrödinger equation of order \(\alpha \in ( 0 , 1 )\)
• Global Analysis of a Model for Capillary Water Waves in Two Dimensions
• Quasi-Töplitz Functions in KAM Theorem
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• KAM Theory for Partial Differential Equations
• Quasi-Periodic Solutions for 1D Schrödinger Equations with Higher Order Nonlinearity
• An integrable normal form for water waves in infinite depth

This page was built for publication: Normal form for the fractional nonlinear Schrödinger equation with cubic nonlinearity