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

1990/02/01 by C. Eugene Wayne · 22 citations
Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum Mechanics and Non-Hermitian Physics #Cold Atom Physics and Bose-Einstein Condensates

paper · doi:10.1007/bf02104499

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• Newton's method and periodic solutions of nonlinear wave equations
• Resonances, radiation damping and instabilitym in Hamiltonian nonlinear wave equations
• Time quasi-periodic vortex patches of Euler equation in the plane
• The stability of full dimensional KAM tori for nonlinear Schrödinger equation
• A KAM theorem for the Hamiltonian with finite zero normal frequencies and its applications
• On the existence of full dimensional KAM tori for 1D periodic nonlinear Schrödinger equation
• Invariant sets through resonant normal form for infinite dimensional holomorphic vector fields
• A Birkhoff--Lewis Type Theorem for Some Hamiltonian Pdes
• Stability of KAM tori for nonlinear Schrodinger equation
• On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range
• Periodic Solutions to Nonlinear Euler-Bernoulli Beam Equations
• Degenerate elliptic resonances
• Periodic solutions to Klein-Gordon systems with linear couplings
• A reducibility result for a class of linear wave equations on\n mathbbT^d
• Quasi-periodic solutions of completely resonant forced wave equations
• KAM for the nonlinear wave equation on the circle: small amplitude solution
• KAM for quasi-linear forced hamiltonian NLS
• The Existence of full dimensional tori for d-dimensional Nonlinear SchrOdinger equation
• On the Stability of Periodic Multi-Solitons of the KdV Equation. [europepmc]
• Space Quasi-Periodic Steady Euler Flows Close to the Inviscid Couette Flow. [europepmc]
• A KAM Approach to the Inviscid Limit for the 2D Navier-Stokes Equations. [europepmc]
• Two-layer model via non-quasi-periodic normal form theory. [europepmc]