Quasi-periodic solutions for the reversible derivative nonlinear Schrödinger equations with periodic boundary conditions

DOI10.1007/s10884-015-9481-7zbMath1377.37109OpenAlexW2185168816MaRDI QIDQ1679052

Zhaowei Lou, Jian-guo Si

Publication date: 8 November 2017

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-015-9481-7

zbMATH Keywords

periodic boundary conditionsquasi-periodic solutionKAM theoremreversible vector field

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to PDEs (35B15) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items

Invariant tori of full dimension for higher-dimensional beam equations with almost-periodic forcing ⋮ Invariant tori for the derivative nonlinear Schrödinger equation with nonlinear term depending on spatial variable ⋮ Invariant tori for reversible nonlinear Schrödinger equations under quasi-periodic forcing ⋮ Kolmogorov-Arnold-Moser theorem for nonlinear beam equations with almost-periodic forcing ⋮ Unnamed Item ⋮ Periodic dynamics of a derivative nonlinear Schrödinger equation with variable coefficients ⋮ Periodic and quasi-periodic solutions for reversible unbounded perturbations of linear Schrödinger equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• KAM for autonomous quasi-linear perturbations of mKdV
• KAM for quasi-linear KdV
• KAM for the quantum harmonic oscillator
• A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations
• A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces
• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• KAM for the nonlinear Schrödinger equation
• The finite-dimensional reversible KAM theory
• Reversible systems
• On small-denominators equations with large variable coefficients
• KAM tori for 1D nonlinear wave equations with periodic boundary conditions
• 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
• Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations
• KAM for the derivative nonlinear Schrödinger equation with periodic boundary conditions
• KAM for reversible derivative wave equations
• A KAM theorem for reversible systems of infinite dimension
• Convergent series expansions for quasi-periodic motions
• KAM theory for the Hamiltonian derivative wave equation
• Quasi-Töplitz Functions in KAM Theorem
• Real analytic quasi-periodic solutions for the derivative nonlinear Schrödinger equations
• KAM tori for reversible partial differential equations
• Spectrum for quantum duffing oscillator and small-divisor equation with large-variable coefficient
• Formation of singularities for wave equations including the nonlinear vibrating string
• KAM theory for lower dimensional tori within the reversible context 2
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Combination tones for Duffing's equation