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37-XX Dynamical systems and ergodic theory
37Kxx Infinite-dimensional Hamiltonian systems
37K50 Bifurcation problems

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Quasi-periodic solutions of Hamiltonian PDEs

Massimiliano Berti (2011)

Journées Équations aux dérivées partielles

We overview recent existence results and techniques about KAM theory for PDEs.

Quasi-periodic solutions with Sobolev regularity of NLS on $𝕋^{d}$ with a multiplicative potential

Massimiliano Berti, Philippe Bolle (2013)

Journal of the European Mathematical Society

We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on $𝕋^{d}, d \geq 1$ , finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are $C^{\infty}$ then the solutions are $C^{\infty}$ . The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators...

Currently displaying 1 – 2 of 2

Page 1

Displaying 1 – 2 of 2

Quasi-periodic solutions of Hamiltonian PDEs

Quasi-periodic solutions with Sobolev regularity of NLS on 𝕋 d with a multiplicative potential

Currently displaying 1 – 2 of 2

Quasi-periodic solutions with Sobolev regularity of NLS on $𝕋^{d}$ with a multiplicative potential