KAM for PDEs (Q295299)

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scientific article; zbMATH DE number 6592720

Language	Label	Description	Also known as
English	KAM for PDEs	scientific article; zbMATH DE number 6592720

Statements

scholarly article

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KAM for PDEs (English)

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Massimiliano Berti

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Bollettino dell'Unione Matematica Italiana

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publication date

13 June 2016

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MaRDI profile type

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full work available at URL

https://doi.org/10.1007/s40574-016-0067-z

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Gravity capillary standing water waves

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KAM for autonomous quasi-linear perturbations of mKdV

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KAM for quasi-linear KdV

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Degenerate KAM theory for partial differential equations

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Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

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Birkhoff normal form for partial differential equations with tame modulus

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Branching of Cantor manifolds of elliptic tori and applications to PDEs

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KAM theory for the Hamiltonian derivative wave equation

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KAM for reversible derivative wave equations

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Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions

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Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential

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Quasi-periodic solutions with Sobolev regularity of NLS on \(\mathbb T^d\) with a multiplicative potential

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A Nash-Moser Approach to KAM Theory

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Quasi-periodic solutions of nonlinear Schrödinger equations on \(T^{d}\)

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An abstract Nash-Moser theorem with parameters and applications to PDEs

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An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifolds

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Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves

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Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces

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The nonlinear Klein-Gordon equation on an interval as a perturbed sine-Gordon equation

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Construction of periodic solutions of nonlinear wave equations in higher dimension

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Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations

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Estimates on Green's functions, localization and the quantum kicked rotor model.

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Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)

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Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential

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Anderson localization for time quasi-periodic random Schrödinger and wave equations

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Quasi-periodic solutions of nonlinear random Schrödinger equations

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Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz

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KAM tori for 1D nonlinear wave equations with periodic boundary conditions

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A KAM result on compact Lie groups

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Hamiltonian long‐wave expansions for free surfaces and interfaces

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Traveling Two and Three Dimensional Capillary Gravity Water Waves

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Numerical simulation of gravity waves

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Mapping properties of normal forms transformations for water waves

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Newton's method and periodic solutions of nonlinear wave equations

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Periodic solutions of nonlinear Schrödinger equations: a paradifferential approach

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Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres

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KAM for the nonlinear beam equation

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On reducibility of Schrödinger equations with quasiperiodic in time potentials

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KAM for the nonlinear Schrödinger equation

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Perturbatively unstable eigenvalues of a periodic Schrödinger operator

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Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations

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Démonstration du ‘théorème d'Arnold’ sur la stabilité du système planétaire (d'après Herman)

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A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces

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An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation

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Periodic solutions for a class of nonlinear partial differential equations in higher dimension

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KAM for the Klein Gordon equation on \(\mathbb {S}^d\)

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Perturbations of the defocusing nonlinear Schrödinger equation

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The defocusing NLS equation and its normal form

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KAM for the quantum harmonic oscillator

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Multimodal standing gravity waves: a completely resonant system

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Existence of multimodal standing gravity waves

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Small divisor problem in the theory of three-dimensional water gravity waves

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Asymmetrical three-dimensional travelling gravity waves

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Standing waves on an infinitely deep perfect fluid under gravity

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Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations

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A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations

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An inverse function theorem in Frechet-spaces

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A KAM theorem for the defocusing NLS equation

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Strong nonresonance of Schrödinger operators and an averaging theorem

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Global Well-Posedness of mKdV in<i>L</i><sup>2</sup>(𝕋, ℝ)

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Formation of singularities for wave equations including the nonlinear vibrating string

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Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation

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Convergent series expansions for quasi-periodic motions

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Nash-Moser theory for standing water waves.

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On elliptic lower dimensional tori in Hamiltonian systems

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Quasi-periodic solutions for a nonlinear wave equation

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A normal form for the Schrödinger equation with analytic non-linearities

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A KAM algorithm for the resonant non-linear Schrödinger equation

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Reducible quasi-periodic solutions for the non linear Schrödinger equation

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Quasi-Töplitz functions in KAM theorem

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Diophantine approximations on submanifolds of Euclidean space

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Periodic solutions of hamiltonian systems

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Invariant tori in non-degenerate nearly integrable Hamiltonian systems

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Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory

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KAM tori for reversible partial differential equations

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S40574-016-0067-Z

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Sitelinks

Mathematics(1 entry)

mardi Publication:295299

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