Birkhoff Normal Form for PDEs and related results

1. D. Bambusi, S. Cuccagna, On dispersion of small energy solutions of the nonlinear Klein Gordon equation with a potential, Preprint 2009
   
2. D. Bambusi, A Birkhoff normal form theorem for some nonlinear PDEs. Preprint 2007 (Lecture notes Montreal).
   
3. D.Bambusi: Galerkin averaging method and Poincare' normal form for some quasilinear PDEs.   Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4 (2005), no. 4, 669--702
4. D.Bambusi, B. Grebert: Birkhoff normal form for PDEs with tame modulus. Duke Math. J. 135, (3) (2006) 507-567.
   
5. D. Bambusi: Nekhoroshev theorem for small amplitude solutions in nonlinear Schroedinger equations. Math. Z., 130, 345-387, (1999).
   
6. D. Bambusi, N.N Nekhoroshev: A property of exponential stability in the nonlinear wave equation close to main linear mode. Physica D, 122, 73-104 (1998).

1. D. Bambusi, C. Bardelle: Invariant tori for commuting Hamiltonian PDEs. To appear in J. Diff. Equations.
   
2. D. Bambusi: Families of periodic solutions of reversible PDEs. Appendix to "Hamiltonian PDEs" by S. Kuksin. Handbook of Dynamical Systems, Vol 1B. Edited by B. Hasselblatt and A. Katok, Elsevier (2006).
   
3. D. Bambusi, M. Berti: A Birkhoff--Lewis Type theorem for some Hamiltonian PDEs. SIAM J. of Math. Analysis. 37, 83--102 (2005).

Chains of particles and FPU problem

1. D. Bambusi, S. Paleari, T. Penati: Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices. Preprint 2009
   
2. D. Bambusi, T. Penati, Continuous approximation of breathers in one and two dimensional DNLS lattices, Preprint 2009
   
3. Dario Bambusi, Thomas Kappeler, Thierry Paul. De Toda à KdV. Preprint 2009.
   
4. D. Bambusi, A. Carati, T. Penati: Boundary effects on the dynamics of chains of coupled oscillators. To appear in Nonlinearity.
   
5. D. Bambusi, A. Ponno: On metastability in FPU. Comm. Math. Phys. 264 (2006), no. 2, 539--561.
6. D. Bambusi: Exponential Stability of breathers in Hamiltonian Networks of Weakly Coupled Oscillators, Nonlinearity, 9 (1996).
7. D. Bambusi, A. Giorgilli: Exponential stability of states close to resonance in infinite dimensional hamiltonian systems. Jour. Stat. Phys.: 71 p. 569 (1993).

Semiclassical limit  
 

1. D. Bambusi, A. Sacchetti: Exponential times in the one-dimensional Gross--Petaevskii equation with multiple well potential. Commun. Math. Phys. 2007.
   
2. D. Bambusi: Normal forms and semi-classical approximation. To appear in Encyclopdia of Mathematical Physics.
   
3. D. Bambusi, S. Graffi, T. Paul: Normal forms and quantization formulae. Commun. Math. Phys., 207, 173-195, (1999).
4. D. Bambusi, S. Graffi, T. Paul: Long time semiclassical approximation of quantum flows: a proof of the Ehrenfest time, Asymptotic Anal., 21, 149-160 (1999).

Last update  11/09/09