Birkhoff normal form for the derivative nonlinear Schrödinger equation

DOI10.1007/s10114-022-0472-4zbMath1490.37092arXiv2009.11236OpenAlexW4225728022MaRDI QIDQ2075439

Jian-Jun Liu

Publication date: 14 February 2022

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.11236

zbMATH Keywords

Birkhoff normal formderivative nonlinear Schrödinger equationlong-time stability

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Cites Work

• Unnamed Item
• Birkhoff normal form for partial differential equations with tame modulus
• Normal forms for semilinear quantum harmonic oscillators
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Birkhoff normal form for some nonlinear PDEs
• On diffusion in high-dimensional Hamiltonian systems and PDE
• Almost global solutions of capillary-gravity water waves equations on the circle
• Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
• Rational normal forms and stability of small solutions to nonlinear Schrödinger equations
• Long time dynamics for generalized Korteweg-de Vries and Benjamin-Ono equations
• The defocusing NLS equation and its normal form
• KAM for the derivative nonlinear Schrödinger equation with periodic boundary conditions
• A Nekhoroshev-type theorem for the nonlinear Schrödinger equation on the torus
• Invariant Cantor manifolds of quasi-periodic solutions for the derivative nonlinear Schrödinger equation
• Averaging principle for the KdV equation with a small initial value
• Modified Nonlinear Schrödinger Equation for Alfvén Waves Propagating along the Magnetic Field in Cold Plasmas
• Stability of KAM tori for nonlinear Schrödinger equation
• An exact solution for a derivative nonlinear Schrödinger equation
• Long Time Stability of Hamiltonian Partial Differential Equations
• Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres
• Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds