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Publications Influence

Birkhoff Normal Form for Some Nonlinear PDEs

- D. Bambusi
- Mathematics
- 1 March 2003

Abstract: We consider the problem of extending to PDEs Birkhoff normal form theorem on Hamiltonian systems close to nonresonant elliptic equilibria. As a model problem we take the nonlinear wave… Expand

139 22

Birkhoff normal form for partial differential equations with tame modulus

- D. Bambusi, B. Grébert
- Mathematics
- 1 December 2006

We prove an abstract Birkhoff normal form theorem for Hamiltonian Partial Differential Equations. The theorem applies to semilinear equations with nonlinearity satisfying a property that we call of… Expand

156 14

On dispersion of small energy solutions of the nonlinear Klein Gordon equation with a potential

- D. Bambusi, Dario Scipio Cuccagna
- Physics, Mathematics
- 31 August 2009

In this paper we study small amplitude solutions of nonlinear Klein Gordon equations with a potential. Under suitable smoothness and decay assumptions on the potential and a genericity assumption on… Expand

50 10- PDF

A Birkhoff normal form theorem for some semilinear PDEs

- D. Bambusi
- Mathematics
- 2008

In these lectures we present an extension of Birkhoff normal form theorem to some Hamiltonian PDEs. The theorem applies to semilinear equations with non- linearity of a suitable class. We present an… Expand

50 8

Nekhoroshev theorem for small amplitude solutions in nonlinear Schrödinger equations

- D. Bambusi
- Mathematics
- 1 February 1999

Abstract. We prove a Nekhoroshev type result [26,27] for the nonlinear Schrödinger equation
\begin{eqnarray} iu_t=-u_{xx}-mu-u \varphi (|u|^2) , \end{eqnarray} with vanishing or periodic boundary… Expand

75 8

Reducibility of the Quantum Harmonic Oscillator in $d$-dimensions with Polynomial Time Dependent Perturbation

- D. Bambusi, B. Grébert, A. Maspero, D. Robert
- Mathematics, Physics
- 17 February 2017

We prove a reducibility result for a quantum harmonic oscillator in arbitrary dimensions with arbitrary frequencies perturbed by a linear operator which is a polynomial of degree two in $x_j$, $-i… Expand

56 5- PDF

Families of Periodic Solutions of Resonant PDEs

- D. Bambusi, S. Paleari
- Mathematics, Computer Science
- J. Nonlinear Sci.
- 1 February 2001

TLDR

57 4

Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

- D. Bambusi, J. Delort, B. Grébert, J. Szeftel
- Mathematics
- 14 October 2005

This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the… Expand

91 4- PDF

On long time stability in Hamiltonian perturbations of non-resonant linear PDEs

- D. Bambusi
- Mathematics
- 1 July 1999

We consider small Hamiltonian perturbations of a system of infinitely many harmonic oscillators. We assume that the frequencies j, j 1, fulfil j ~ jd with d 1, and a suitable non-resonance condition… Expand

53 4

Time Quasi-Periodic Unbounded Perturbations¶of Schrödinger Operators and KAM Methods

- D. Bambusi, S. Graffi
- Physics, Mathematics
- 2 October 2000

Abstract: We eliminate by KAM methods the time dependence in a class of linear differential equations in ℓ2 subject to an unbounded, quasi-periodic forcing. This entails the pure-point nature of the… Expand

100 4- PDF

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