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

1990/02/01 by C. Eugene Wayne · 468 citations
Mathematics · Physics and Astronomy · #Class (philosophy) #Cold Atom Physics and Bose-Einstein Condensates #Hamiltonian system #Kolmogorov–Arnold–Moser theorem #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Periodic wave #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quasi periodic #Traveling wave

paper · doi:10.1007/bf02104499

published in Communications in Mathematical Physics 127(3), 479-528 (Springer Science+Business Media)

openalex publication_date 1990/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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• On the existence of full dimensional KAM tori for 1D periodic nonlinear Schrödinger equation
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• 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 \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
• Lindstedt series for periodic solutions of beam equations with quadratic and velocity dependent nonlinearities
• Quasi-Periodic Solutions For Nonlinear Klein-Gordon Equations
• On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces
• Response solutions for wave equations with variable wave speed and periodic forcing
• The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation
• On dispersion of small energy solutions of the nonlinear Klein Gordon equation with a potential
• Birkhoff normal form via decorated trees
• Two Layer Model via Non Quasi Periodic Normal Form Theory
• Long time behavior of solutions for a damped Benjamin-Ono equation
• Invariant Cantor manifolds of quasi-periodic solutions for the derivative nonlinear Schrodinger equation
• On periodic solutions of nonlinear wave equations, including Einstein\n equations with a negative cosmological constant
• On almost periodic solutions to NLS without external parameters
• The Existence of Full-Dimensional KAM tori for one-dimensional nonlinear Klein-Gordon equation
• Dynamics of Nonlinear Waves on Bounded Domains
• Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity
• KAM tori for the generalized Bejamin-Bona-Mahony equation
• Analytic solutions of nonlinear elliptic equations on rectangular tori
• Quasi-periodic solutions to nonlinear beam equation on Compact Lie Groups with a multiplicative potential
• Reducibility of 1-d Schrödinger Equation with Time Quasiperiodic Unbounded Perturbations, II
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