The problem of persistence of invariant tori in infinite dimension is a challenging problem in the study of PDEs. There is a rather well established literature on the persistence of n-dimensional invariant tori carrying a quasi-periodic Diophantine flow (for one-dimensional system) but very few on the persistence of infinite-dimensional ones. Inspired by the classical "twisted conjugacy theorem" of M. Herman for perturbations of degenerate Hamiltonians possessing a Diophantine invariant torus, we intend to present a compact and unified frame in which recover the results of Bourgain and Pà ¶schel on the existence of almost-periodic solutions for the Nonlinear Schrà ¶dinger equation. We shall discuss the main advantages of our approach as w...
Motivated by the problem of long time stability vs. instability of KAM tori of the Nonlinear cubic S...
AbstractConsider the NLS with periodic boundary conditions in 1D(0.1)iut+Δu+Mu±ɛu|u|4=0,where M is a...
In this paper, one-dimensional (1D) nonlinear Schrödinger equation iut −uxx +|u | 2p u = 0, p ∈ N, w...
The problem of persistence of invariant tori in infinite dimension is a challenging problem in the s...
In this paper we study the existence and linear stability of almost periodic solutions for a NLS equ...
We prove that many finite dimensional tori, invariant under the flow of the defocusing nonlinear Sch...
AbstractIn this paper, we consider one-dimensional nonlinear Schrödinger equation iut−uxx+V(x)u+f(|u...
We prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\u7foding...
We consider the defocusing cubic nonlinear Schrà ¶dinger equation (NLS) on the two-dimensional toru...
AbstractIn this paper, one-dimensional (1D) nonlinear Schrödinger equationiut−uxx+|u|2pu=0,p∈N, with...
AbstractIn this paper, we consider the one-dimensional nonlinear Schrödinger equationiut−uxx+mu+f(|u...
In this note we describe the construction of almost-periodic solutions for a nonlinear Schrödinger ...
We consider families of dynamical systems having invariant tori that carry quasi-periodic motions. O...
Abstract. The celebrated theorem of Kolmogorov on persistence of invariant tori of a nearly integrab...
This paper is devoted to the construction of periodic solutions of nonlinear Schrödinger equations o...
Motivated by the problem of long time stability vs. instability of KAM tori of the Nonlinear cubic S...
AbstractConsider the NLS with periodic boundary conditions in 1D(0.1)iut+Δu+Mu±ɛu|u|4=0,where M is a...
In this paper, one-dimensional (1D) nonlinear Schrödinger equation iut −uxx +|u | 2p u = 0, p ∈ N, w...
The problem of persistence of invariant tori in infinite dimension is a challenging problem in the s...
In this paper we study the existence and linear stability of almost periodic solutions for a NLS equ...
We prove that many finite dimensional tori, invariant under the flow of the defocusing nonlinear Sch...
AbstractIn this paper, we consider one-dimensional nonlinear Schrödinger equation iut−uxx+V(x)u+f(|u...
We prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\u7foding...
We consider the defocusing cubic nonlinear Schrà ¶dinger equation (NLS) on the two-dimensional toru...
AbstractIn this paper, one-dimensional (1D) nonlinear Schrödinger equationiut−uxx+|u|2pu=0,p∈N, with...
AbstractIn this paper, we consider the one-dimensional nonlinear Schrödinger equationiut−uxx+mu+f(|u...
In this note we describe the construction of almost-periodic solutions for a nonlinear Schrödinger ...
We consider families of dynamical systems having invariant tori that carry quasi-periodic motions. O...
Abstract. The celebrated theorem of Kolmogorov on persistence of invariant tori of a nearly integrab...
This paper is devoted to the construction of periodic solutions of nonlinear Schrödinger equations o...
Motivated by the problem of long time stability vs. instability of KAM tori of the Nonlinear cubic S...
AbstractConsider the NLS with periodic boundary conditions in 1D(0.1)iut+Δu+Mu±ɛu|u|4=0,where M is a...
In this paper, one-dimensional (1D) nonlinear Schrödinger equation iut −uxx +|u | 2p u = 0, p ∈ N, w...