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KAM theorem for the nonlinear Schrödinger equation. (Théorème de type KAM pour l’équation de Schrödinger non linéaire.) (French. Abridged English version) Zbl 0913.35125

Summary: We prove the persistence of finite-dimensional invariant tori associated with the defocusing nonlinear Schrödinger equation \[ i\partial_t\varphi= -\partial^2_{xx}\varphi+ 2|\varphi|^2 \varphi\quad (t\in\mathbb{R}, x\in S^1) \] under small Hamiltonian perturbations. The invariant tori are not necessarily small.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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