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D. Bambusi

  1. Continuous approximation of breathers in one and two dimensional DNLS lattices.

    Fri, 09/11/2009 - 19:12 — SomNambul
    Authors: D. Bambusi, T. Penati
    Subjects: Dynamical Systems
    Abstract

    In this paper we construct and approximate breathers in the DNLS model
    starting from the continuous limit: such periodic solutions are obtained as
    perturbations of the ground state of the NLS model in $H^1(\RR^n)$, with
    $n=1,2$. In both the dimensions we recover the Sievers-Takeno (ST) and the Page
    (P) modes; furthermore, in $\RR^2$ also the two hybrid (H) modes are
    constructed. The proof is based on the interpolation of the lattice using the
    Finite Element Method (FEM).

  2. Continuous approximation of breathers in one and two dimensional DNLS lattices.

    Fri, 09/11/2009 - 19:12 — SomNambul
    Authors: D. Bambusi, T. Penati
    Subjects: Dynamical Systems
    Abstract

    In this paper we construct and approximate breathers in the DNLS model
    starting from the continuous limit: such periodic solutions are obtained as
    perturbations of the ground state of the NLS model in $H^1(\RR^n)$, with
    $n=1,2$. In both the dimensions we recover the Sievers-Takeno (ST) and the Page
    (P) modes; furthermore, in $\RR^2$ also the two hybrid (H) modes are
    constructed. The proof is based on the interpolation of the lattice using the
    Finite Element Method (FEM).

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

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: D. Bambusi, S. Cuccagna
    Subjects: Analysis of PDEs
    Abstract

    In this paper we study small amplitude solutions of nonlinear Klein Gordon
    equations with a potential. Under smoothness and decay assumptions on the
    potential and a genericity assumption on the nonlinearity, we prove that all
    small amplitude initial data with finite energy give rise to solutions
    asymptotically free. In the case where the linear system has at most one bound
    state the result was already proved by Soffer and Weinstein: we obtain here a
    result valid in the case of an arbitrary number of possibly degenerate bound
    states.

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