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Communication Dans Un Congrès Année : 2008

Four lectures on KAM for the non-linear Schrödinger equation

Résumé

We discuss the KAM-theory for lower-dimensional tori for the non-linear Schrödinger equation with periodic boundary conditions and a convolution potential in dimension d. Central in this theory is the homological equation and a condition on the small divisors often known as the second Melnikov condition. The difficulties related to this condition are substantial when d≥ 2. We discuss this difficulty, and we show that a block decomposition and a Töplitz- Lipschitz-property, present for non-linear Schrödinger equation, permit to overcome this difficuly. A detailed proof is given in [EK06].

Dates et versions

hal-00832727 , version 1 (11-06-2013)

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Hakan Eliasson, Sergei Kuksin. Four lectures on KAM for the non-linear Schrödinger equation. Hamiltonian dynamical systems, 2007, Montréal, Canada. pp.179-212, ⟨10.1007/978-1-4020-6964-2_10⟩. ⟨hal-00832727⟩
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