KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation
By Pierre Baldi, Massimiliano Berti, Riccardo Montalto. 2014
187 citations recorded by the source corpus.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/391a8957bdcec8451c16a01b791284e5a55b3526
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
- Massimiliano Berti
- Michela Procesi
- Riccardo Montalto
- Pierre Baldi
- R. Feola
- E. Haus
- Felice Iandoli
- Filippo Giuliani
Citations in the corpus
- Growth of Sobolev norms for abstract linear Schrödinger equations (2017, methodology): “Sobolev norms in higher dimensional systems without any gap condition. The proof is based on the combination of the ideas of [Bam17a, Bam17b, BGMR17] (which in turn are a developments of the ideas of [BBM14], see also [PT01, IPT05]) and the results of [MR17]; precisely, for any positive N, we constr”
- KAM for autonomous quasi-linear perturbations of mKdV (2014, methodology): “Major differences with respect to [2] for transforming (1.”
- Time quasi-periodic gravity water waves in finite depth (2017, methodology): “For quasi-linear (either fully nonlinear) nonlinearities the first KAM results have been recently proved by Baldi-Berti-Montalto in [7], [8], [9] for perturbations of Airy, KdV and mKdV equations.”
- Long time existence for fully nonlinear NLS with small Cauchy data on the circle (2018, methodology): “A related regularization procedure of the unbounded terms of the equations has been previously developed in order to study the linearized equation associated to a quasi-linear system in the context of a Nash-Moser iterative scheme (see for instance [1, 8, 2, 3, 17, 18]).”
- Reducibility of first order linear operators on tori via Moser's theorem (2018, methodology): “, O s +C(kukγ,O s |p| O 1,∞ +|p| γ,O s,∞kuk γ, 2 ), s ∈ N (A.8) the constant C depends on d,s (it is independent on γ). Proof. The estimate (A.5) is proved in [3], (A.6b) is proved in the Appendix of [5]. The bounds (A.6a) are slightly different from the corresponding ones of [3], [5]. This and the d”