KAM for PDEs
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Publication:295299
DOI10.1007/s40574-016-0067-zzbMath1339.37075OpenAlexW2318661185MaRDI QIDQ295299
Publication date: 13 June 2016
Published in: Bollettino dell'Unione Matematica Italiana (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s40574-016-0067-z
PDEs in connection with fluid mechanics (35Q35) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations in context of PDEs (35B20) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)
Related Items (8)
Whitney smooth families of invariant tori within the reversible context 2 of KAM theory ⋮ Reducibility of quantum harmonic oscillator on $\mathbb{R}^d$ with differential and quasi-periodic in time potential ⋮ Reducibility of 1-d quantum harmonic oscillator equation with unbounded oscillation perturbations ⋮ On time periodic solutions to the conformal cubic wave equation on the Einstein cylinder ⋮ Quasi-periodic incompressible Euler flows in 3D ⋮ Quasi-periodic water waves ⋮ The Navier-Stokes equation with time quasi-periodic external force: existence and stability of quasi-periodic solutions ⋮ KAM for the nonlinear wave equation on the circle: a normal form theorem
Cites Work
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- KAM for autonomous quasi-linear perturbations of mKdV
- Reducible quasi-periodic solutions for the non linear Schrödinger equation
- KAM for the Klein Gordon equation on \(\mathbb {S}^d\)
- Mapping properties of normal forms transformations for water waves
- KAM for quasi-linear KdV
- A KAM algorithm for the resonant non-linear Schrödinger equation
- Degenerate KAM theory for partial differential equations
- An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation
- Quasi-periodic solutions of nonlinear Schrödinger equations on \(T^{d}\)
- Branching of Cantor manifolds of elliptic tori and applications to PDEs
- Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces
- KAM for the quantum harmonic oscillator
- A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations
- Numerical simulation of gravity waves
- A normal form for the Schrödinger equation with analytic non-linearities
- Asymmetrical three-dimensional travelling gravity waves
- KAM for the nonlinear beam equation
- On reducibility of Schrödinger equations with quasiperiodic in time potentials
- A KAM theorem for the defocusing NLS equation
- Existence of multimodal standing gravity waves
- An abstract Nash-Moser theorem with parameters and applications to PDEs
- Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions
- A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces
- Birkhoff normal form for partial differential equations with tame modulus
- Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
- Anderson localization for time quasi-periodic random Schrödinger and wave equations
- KAM for the nonlinear Schrödinger equation
- On elliptic lower dimensional tori in Hamiltonian systems
- An inverse function theorem in Frechet-spaces
- Perturbatively unstable eigenvalues of a periodic Schrödinger operator
- Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
- KAM tori for 1D nonlinear wave equations with periodic boundary conditions
- Invariant tori in non-degenerate nearly integrable Hamiltonian systems
- Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential
- Multimodal standing gravity waves: a completely resonant system
- Estimates on Green's functions, localization and the quantum kicked rotor model.
- Perturbations of the defocusing nonlinear Schrödinger equation
- The nonlinear Klein-Gordon equation on an interval as a perturbed sine-Gordon equation
- Strong nonresonance of Schrödinger operators and an averaging theorem
- Construction of periodic solutions of nonlinear wave equations in higher dimension
- Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
- Quasi-periodic solutions for a nonlinear wave equation
- Quasi-periodic solutions with Sobolev regularity of NLS on \(\mathbb T^d\) with a multiplicative potential
- Periodic solutions of nonlinear Schrödinger equations: a paradifferential approach
- An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifolds
- A KAM result on compact Lie groups
- Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations
- Gravity capillary standing water waves
- Periodic solutions for a class of nonlinear partial differential equations in higher dimension
- The defocusing NLS equation and its normal form
- KAM for reversible derivative wave equations
- Quasi-periodic solutions of nonlinear random Schrödinger equations
- Convergent series expansions for quasi-periodic motions
- Diophantine approximations on submanifolds of Euclidean space
- Standing waves on an infinitely deep perfect fluid under gravity
- A Nash-Moser Approach to KAM Theory
- KAM theory for the Hamiltonian derivative wave equation
- Quasi-Töplitz Functions in KAM Theorem
- Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential
- KAM tori for reversible partial differential equations
- Small divisor problem in the theory of three-dimensional water gravity waves
- Formation of singularities for wave equations including the nonlinear vibrating string
- Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz
- Periodic solutions of hamiltonian systems
- Newton's method and periodic solutions of nonlinear wave equations
- Traveling Two and Three Dimensional Capillary Gravity Water Waves
- Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
- Global Well-Posedness of mKdV inL2(𝕋, ℝ)
- Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves
- Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres
- Démonstration du ‘théorème d'Arnold’ sur la stabilité du système planétaire (d'après Herman)
- Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds
- Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
- Hamiltonian long‐wave expansions for free surfaces and interfaces
- Nash-Moser theory for standing water waves.
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