TY - JOUR
T1 - Existence and stability of quasi-periodic solutions for derivative wave equations
JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Y1 - 2013
A1 - Massimiliano Berti
A1 - Luca Biasco
A1 - Michela Procesi
KW - Constant coefficients
KW - Dynamical systems
KW - Existence and stability
KW - Infinite dimensional
KW - KAM for PDEs
KW - Linearized equations
KW - Lyapunov exponent
KW - Lyapunov methods
KW - Quasi-periodic solution
KW - Small divisors
KW - Wave equations
AB - In this note we present the new KAM result in [3] which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. In turn, this result is derived by an abstract KAM theorem for infinite dimensional reversible dynamical systems*.
VL - 24
N1 - cited By (since 1996)0
ER -
TY - JOUR
T1 - A note on KAM theory for quasi-linear and fully nonlinear forced KdV
JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437–450
Y1 - 2013
A1 - P Baldi
A1 - Massimiliano Berti
A1 - Riccardo Montalto
KW - KAM for PDEs
AB - We present the recent results in [3] concerning quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities the solutions are linearly stable. The proofs are based on a combination of di erent ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a di erential operator with constant coe cients plus a bounded remainder. These transformations are obtained by changes of variables induced by di eomorphisms of the torus and pseudo-di erential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coe cients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues.
PB - European Mathematical Society
U1 - 7268
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -