KAM for autonomous quasi-linear perturbations of mKdV

By Pierre Baldi, Massimiliano Berti, Riccardo Montalto. 2014

126 citations recorded by the source corpus.

We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear (also called strongly nonlinear) autonomous Hamiltonian differentiable perturbations of the mKdV equation. The proof is based on a weak version of the Birkhoff normal form algorithm and a nonlinear Nash–Moser iteration. The analysis of the linearized operators at each step of the iteration is achieved by pseudo-differential operator techniques and a linear KAM reducibility scheme.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/495e0a84877928958338674fe93fe50ed372d4ab

How researchers see this paper

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In Numerical Analysis

1. Pierre Baldi
2. E. Haus
3. Riccardo Montalto
4. Massimiliano Berti
5. P. Bolle

In Statistical and Nonlinear Physics

1. Riccardo Montalto
2. Pierre Baldi
3. Massimiliano Berti
4. E. Haus
5. Michela Procesi
6. P. Bolle
7. R. Feola
8. Filippo Giuliani

Citations in the corpus

• 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.”