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J. Geng, Jian Wu (2012)
Real analytic quasi-periodic solutions for the derivative nonlinear Schrödinger equationsJournal of Mathematical Physics, 53
Jurgen Poschel (2007)
Quasi-periodic solutions for a nonlinear wave equation
Jianjun Liu, Xiaoping Yuan (2014)
KAM for the derivative nonlinear Schrödinger equation with periodic boundary conditionsJournal of Differential Equations, 256
M Berti, L Biasco, M Procesi (2013)
KAM theory for the Hamiltonian derivative wave equationAnn. Sci. Éc. Norm. Supér. (4), 46
Jurgen Poschel (2009)
A lecture on the classical KAM theoremarXiv: Dynamical Systems
R. Feola, M. Procesi (2014)
Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equationsJournal of Differential Equations, 259
S Kuksin (1998)
A KAM-theorem for equations of the Korteweg-de Vries typeRev. Math. Math. Phys, 10
M. Berti, L. Biasco, M. Procesi (2012)
KAM for Reversible Derivative Wave EquationsArchive for Rational Mechanics and Analysis, 212
S. Kuksin (1997)
On small-denominators equations with large variable coefficientsZeitschrift für angewandte Mathematik und Physik ZAMP, 48
P. Baldi, M. Berti, Riccardo Montalto (2014)
KAM for quasi-linear KdVComptes Rendus Mathematique, 352
M. Sevryuk (1998)
The finite-dimensional reversible KAM theoryPhysica D: Nonlinear Phenomena, 112
Jianjun Liu, Xiaoping Yuan (2011)
A KAM Theorem for Hamiltonian Partial Differential Equations with Unbounded PerturbationsCommunications in Mathematical Physics, 307
S. Kuksin (1998)
A KAM-theorem for equations of the Korteweg--de Vries typeReviews in Mathematical Physics, 10
(1986)
Reversible Systems
Jie Liu, Jianguo Si (2016)
Invariant tori of a nonlinear Schrödinger equation with quasi-periodically unbounded perturbationsCommunications on Pure and Applied Analysis, 16
Ihrer Grenzgebiete, Theorie Der, Konvexen Körper (1975)
Ergebnisse der Mathematik und ihrer GrenzgebieteSums of Independent Random Variables
P. Baldi, M. Berti, Riccardo Montalto (2014)
KAM for quasi-linear and fully nonlinear forced perturbations of Airy equationMathematische Annalen, 359
N. Bogoljubov, A. Samoilenko, Ju. Mitropoliskii (1976)
Methods of Accelerated Convergence in Nonlinear Mechanics
Jie Liu, Jianguo Si (2015)
Invariant tori for a derivative nonlinear Schrödinger equation with quasi-periodic forcingJournal of Mathematical Physics, 56
TP Kappeler, J Pöschel (2003)
KdV & KAM, volume 45 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics (Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics)
Lufang Mi, K. Zhang (2013)
Invariant Tori for Benjamin-Ono Equation with Unbounded quasi-periodically forced PerturbationDiscrete and Continuous Dynamical Systems, 34
Jing Zhang, M. Gao, Xiaoping Yuan (2011)
KAM tori for reversible partial differential equationsNonlinearity, 24
Zhaowei Lou, Jianguo Si (2017)
Quasi-Periodic Solutions for the Reversible Derivative Nonlinear Schrödinger Equations with Periodic Boundary ConditionsJournal of Dynamics and Differential Equations, 29
In this paper, by infinite-dimensional reversible KAM (Kolmogorov–Arnold–Moser) theory, we prove the existence of invariant tori (thus quasi-periodic solutions) for a class of quasi-periodically forced reversible derivative nonlinear Schrödinger equations under periodic and Dirichlet boundary conditions. In the proof, we also use Birkhoff normal form techniques.
Zeitschrift für angewandte Mathematik und Physik – Springer Journals
Published: Aug 14, 2017
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