Real analytic quasi-periodic solutions for the derivative nonlinear Schrödinger equations

DOI10.1063/1.4754822zbMath1337.35134OpenAlexW2046125956MaRDI QIDQ2872308

Jian Wu, Jiansheng Geng

Publication date: 14 January 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/550a6debb4cc28aadeb1e347ab35265a313cca6d

zbMATH Keywords

quasi-periodic solutionsKAM theoryderivative nonlinear Schrödinger equation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Higher degree equations; Fermat's equation (11D41) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items (17)

Quasi-periodic solutions for a Schrödinger equation with a quintic nonlinear term depending on the time and space variables ⋮ Invariant tori for the derivative nonlinear Schrödinger equation with nonlinear term depending on spatial variable ⋮ Quasi-periodic solutions for the reversible derivative nonlinear Schrödinger equations with periodic boundary conditions ⋮ Real analytic quasi-periodic solutions with more Diophantine frequencies for perturbed KdV equations ⋮ Invariant tori for reversible nonlinear Schrödinger equations under quasi-periodic forcing ⋮ Invariant tori of full dimension for second KdV equations with the external parameters ⋮ Quasi-periodic solutions for beam equations with the nonlinear terms depending on the space variable ⋮ KAM tori for completely resonant Hamiltonian derivative beam equations on \(\mathbb{T}^2\) ⋮ A KAM theorem for higher dimensional forced nonlinear Schrödinger equations ⋮ Invariant tori of a nonlinear Schrödinger equation with quasi-periodically unbounded perturbations ⋮ KAM tori for the derivative quintic nonlinear Schrödinger equation ⋮ Periodic and quasi-periodic solutions of a derivative nonlinear Schrödinger equation ⋮ Periodic dynamics of a derivative nonlinear Schrödinger equation with variable coefficients ⋮ Periodic and quasi-periodic solutions for reversible unbounded perturbations of linear Schrödinger equations ⋮ Invariant tori for a derivative nonlinear Schrödinger equation with quasi-periodic forcing ⋮ Quasi-periodic solutions for Schrödinger equation with derivative nonlinearity (|u|^2pu)_x ⋮ Reducibility of quasi-periodic linear KdV equation

Cites Work

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• A KAM theorem for one dimensional Schrödinger equation with periodic boundary conditions
• KAM tori of Hamiltonian perturbations of 1D linear beam equations
• Quasi-periodic solutions for a nonlinear wave equation
• KAM tori for reversible partial differential equations
• Spectrum for quantum duffing oscillator and small-divisor equation with large-variable coefficient
• Quasi-Periodic Solutions for 1D Schrödinger Equations with Higher Order Nonlinearity
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Time quasi-periodic unbounded perturbations of Schrödinger operators and KAM methods

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