Invariant Cantor Manifolds of Quasi-Periodic Oscillations for a Nonlinear Schrodinger Equation

1996/01/01 by Sergej Kuksin, Sergej B. Kuksin, Jurgen Poschel +1 · 21 citations
Physics and Astronomy · Computer Science · Mathematics · #Quantum chaos and dynamical systems #Nonlinear Dynamics and Pattern Formation #Spectral Theory in Mathematical Physics

paper · doi:10.2307/2118656

Abstract

Sergej Kuksin, Jurgen Poschel, Invariant Cantor Manifolds of Quasi-Periodic Oscillations for a Nonlinear Schrodinger Equation, Annals of Mathematics, Second Series, Vol. 143, No. 1 (Jan., 1996), pp. 149-179

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• Rational normal forms and stability of small solutions to nonlinear\n Schr "odinger equations
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• Quasi-periodic solutions for perturbed generalized nonlinear vibrating string equation with singularities
• Persistence of Invariant Tori for Stochastic Nonlinear Schrödinger in the Sense of Most Probable Paths
• Linearly Stable KAM Tori for One Dimensional Forced Kirchhoff Equations under Periodic Boundary Conditions
• An infinite-dimensional Kolmogorov theorem and the construction of almost periodic breathers
• KAM for the nonlinear wave equation on the circle: small amplitude solution
• Energy cascades for NLS on the torus
• The Existence of full dimensional tori for d-dimensional Nonlinear SchrOdinger equation
• Sergei B. Kuksin [wikipedia]
• On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations. [europepmc]
• A KAM Approach to the Inviscid Limit for the 2D Navier-Stokes Equations. [europepmc]
• Large Amplitude Quasi-Periodic Traveling Waves in Two Dimensional Forced Rotating Fluids. [europepmc]

Related

• Invariant Cantor manifolds of quasi-periodic solutions for the derivative nonlinear Schrodinger equation
• Infinite energy quasi-periodic solutions to nonlinear Schrödinger equations on \mathbb R
• KAM for quasi-linear autonomous NLS
• Asymptotically full measure sets of almost-periodic solutions for the NLS equation
• Cantor spectrum for a class of C² quasiperiodic Schrödinger operators