KAM for quasi-linear KdV

Pietro Baldi; Massimiliano Berti; Riccardo Montalto

doi:10.1016/j.crma.2014.04.012

Partial differential equations

KAM for quasi-linear KdV

Presented by: Gérard Iooss

Pietro Baldi ¹; Massimiliano Berti ²; Riccardo Montalto ²

¹ Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università di Napoli Federico II, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy
² SISSA, Via Bonomea 265, 34136 Trieste, Italy

Comptes Rendus. Mathématique, Volume 352 (2014) no. 7-8, pp. 603-607.

Abstract
Résumé

We prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

Nous prouvons l'existence de solutions quasi périodiques linéairement stables pour des perturbations hamiltoniennes autonomes quasi linéaires de l'équation KdV.

Received: 2014-04-14
Accepted: 2014-04-30
Published online: 2014-06-04

DOI: 10.1016/j.crma.2014.04.012

Author's affiliations:

Pietro Baldi ¹; Massimiliano Berti ²; Riccardo Montalto ²

¹ Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università di Napoli Federico II, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy
² SISSA, Via Bonomea 265, 34136 Trieste, Italy

@article{CRMATH_2014__352_7-8_603_0,
     author = {Pietro Baldi and Massimiliano Berti and Riccardo Montalto},
     title = {KAM for quasi-linear {KdV}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {603--607},
     publisher = {Elsevier},
     volume = {352},
     number = {7-8},
     year = {2014},
     doi = {10.1016/j.crma.2014.04.012},
     language = {en},
}

TY  - JOUR
AU  - Pietro Baldi
AU  - Massimiliano Berti
AU  - Riccardo Montalto
TI  - KAM for quasi-linear KdV
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 603
EP  - 607
VL  - 352
IS  - 7-8
PB  - Elsevier
DO  - 10.1016/j.crma.2014.04.012
LA  - en
ID  - CRMATH_2014__352_7-8_603_0
ER  -

%0 Journal Article
%A Pietro Baldi
%A Massimiliano Berti
%A Riccardo Montalto
%T KAM for quasi-linear KdV
%J Comptes Rendus. Mathématique
%D 2014
%P 603-607
%V 352
%N 7-8
%I Elsevier
%R 10.1016/j.crma.2014.04.012
%G en
%F CRMATH_2014__352_7-8_603_0

Pietro Baldi; Massimiliano Berti; Riccardo Montalto. KAM for quasi-linear KdV. Comptes Rendus. Mathématique, Volume 352 (2014) no. 7-8, pp. 603-607. doi : 10.1016/j.crma.2014.04.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.04.012/

References
Cited by

[1] P. Baldi Periodic solutions of fully nonlinear autonomous equations of Benjamin–Ono type, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 30 (2013), pp. 33-77

[2] P. Baldi; M. Berti; R. Montalto KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation, Math. Ann., Volume 359 (2014), pp. 471-536 | DOI

[3] P. Baldi; M. Berti; R. Montalto KAM for autonomous quasi-linear perturbations of KdV, 2014 (preprint) | arXiv

[4] M. Berti, P. Bolle, A Nash–Moser approach to KAM theory, preprint, 2014.

[5] G. Iooss; P.I. Plotnikov; J.F. Toland Standing waves on an infinitely deep perfect fluid under gravity, Arch. Ration. Mech. Anal., Volume 177 (2005) no. 3, pp. 367-478

[6] T. Kappeler; J. Pöschel KdV and KAM, Springer, 2003

[7] S. Kuksin A KAM theorem for equations of the Korteweg–de Vries type, Rev. Math. Math. Phys., Volume 10 (1998) no. 3, pp. 1-64

[8] S. Kuksin Analysis of Hamiltonian PDEs, Oxford Lecture Series in Mathematics and Applications, vol. 19, Oxford University Press, 2000

[9] J. Liu; X. Yuan A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations, Commun. Math. Phys., Volume 307 (2011) no. 3, pp. 629-673

[10] J. Pöschel Quasi-periodic solutions for a nonlinear wave equation, Comment. Math. Helv., Volume 71 (1996) no. 2, pp. 269-296

[11] M. Procesi; C. Procesi A normal form for the Schrödinger equation with analytic non-linearities, Commun. Math. Phys., Volume 312 (2012), pp. 501-557

Cited by Sources:

Comments - Policy