89 citations · 264 across the 48 of their papers we have counts for
50 papers · 1 filter
Conditional asymptotic stability of solitary waves of the Euler-Poisson system on the line
Junsik Bae, Scipio Cuccagna, Masaya Maeda
We apply the idea of using a combination of virial inequalities and Kato smoothing, previously applied to NLS and generalized KdV pure power equations to Euler-Poisson: we assume t…
On stabilization at a soliton for generalized Korteweg--De Vries pure power equation for any power
Scipio Cuccagna, Masaya Maeda
We apply our idea, which previously we used in the analysis of the pure power NLS, consisting in spitting the virial inequality method into a large energy inequality combined with…
On the asymptotic stability on the line of ground states of the pure power NLS with
Scipio Cuccagna, Masaya Maeda
We continue our series devoted, after references \cite{CM24D1} and \cite{CM243}, at proving the asymptotic stability of ground states of the pure power Nonlinear Schrödinger equati…
On small energy solutions of the Nonlinear Schrödinger Equation in 1D with a generic trapping potential with a single eigenvalue
Scipio Cuccagna, Masaya Maeda
We prove in dimension a result similar to Soffer and Weinstein Jour. Diff. Eq. 98 (1992) capturing for pure power nonlinearities the whole range of exponents . The proof…
A note on the Fermi Golden Rule constant for the pure power NLS
Scipio Cuccagna, Masaya Maeda
We provide a detailed proof that the Nonlinear Fermi Golden Rule coefficient that appears in our recent proof of the asymptotic stability of ground states for the pure power Nonlin…
On the asymptotic stability of ground states of the pure power NLS on the line at 3rd and 4th order Fermi Golden Rule
Scipio Cuccagna, Masaya Maeda
Assuming as hypotheses the results proved numerically by Chang et al. \cite{Chang} for the exponent , we prove that some of the ground states of the nonlinear Schröding…
The asymptotic stability on the line of ground states of the pure power NLS with
Scipio Cuccagna, Masaya Maeda
For exponents satisfying and only in the context of spatially even solutions we prove that the ground states of the nonlinear Schrödinger equation (NLS) with pur…
Paralinearization and extended lifespan for solutions of the -SQG sharp front equation
Massimiliano Berti, Scipio Cuccagna, Francisco Gancedo +1
In this paper we paralinearize the contour dynamics equation for sharp-fronts of -SQG, for any , close to a circular vortex. This turns out to be a quas…
On asymptotic stability on a center hypersurface at the soliton for even solutions of the NLKG when
Scipio Cuccagna, Masaya Maeda, Federico Murgante +1
We extend the result M. Kowalczyk, Y. Martel, C. Muñoz, JEMS 2022, on the existence, in the context of spatially even solutions, of asymptotic stability on a center hypersurface at…
Small energy stabilization for 1D Nonlinear Klein Gordon Equations
Scipio Cuccagna, Masaya Maeda, Stefano Scrobogna
We give a partial extension to dimension 1 of the result proved by Bambusi and Cuccagna on the absence of small energy real valued periodic solutions for the NLKG in dimension 3. W…
Asymptotic stability of kink with internal modes under odd perturbation
Scipio Cuccagna, Masaya Maeda
We give a sufficient condition, in the spirit of Kowalczyk-Martel-Munoz-Van Den Bosch \cite{KMMvdB21AnnPDE}, for the local asymptotic stability of kinks under odd perturbations. In…
Revisiting asymptotic stability of solitons of nonlinear Schrödinger equations via refined profile method
Scipio Cuccagna, Masaya Maeda
In this paper, we give an alternative proof for the asymptotic stability of solitons for nonlinear Schrödinger equations with internal modes. The novel idea is to use "refined prof…
On selection of standing wave at small energy in the 1D Cubic Schrödinger Equation with a trapping potential
Scipio Cuccagna, Masaya Maeda
Combining virial inequalities by Kowalczyk, Martel and Munoz and Kowalczyk, Martel, Munoz and Van Den Bosch with our theory on how to derive nonlinear induced dissipation on discre…
A note on small data soliton selection for nonlinear Schrödinger equations with potential
Scipio Cuccagna, Masaya Maeda
In this note, we give an alternative proof of the theorem on soliton selection for small energy solutions of nonlinear Schrödinger equations (NLS) which we studied in Anal. PDE 8 (…
A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II
Scipio Cuccagna, Masaya Maeda
We give short survey on the question of asymptotic stability of ground states of nonlinear Schrödinger equations, focusing primarily on the so called nonlinear Fermi Golden Rule.
Coordinates at small energy and refined profiles for the Nonlinear Schrödinger Equation
Scipio Cuccagna, Masaya Maeda
In this paper we give a new and simplified proof of the theorem on selection of standing waves for small energy solutions of the nonlinear Schrödinger equations (NLS) that we gave…
On stability of small solitons of the 1--D NLS with a trapping delta potential
Scipio Cuccagna, Masaya Maeda
We consider a Nonlinear Schrödinger Equation with a very general non linear term and with a trapping potential on the line. We then discuss the asymptotic behavior of all its s…
Long time oscillation of solutions of nonlinear Schrödinger equations near minimal mass ground state
Scipio Cuccagna, Masaya Maeda
In this paper, we consider the long time dynamics of radially symmetric solutions of nonlinear Schrödinger equations (NLS) having a minimal mass ground state. In particular, we sho…
On asymptotic stability of ground states of some systems of nonlinear Schrödinger equations
Andrew Comech, Scipio Cuccagna
We extend to a specific class of systems of nonlinear Schrödinger equations (NLS) the theory of asymptotic stability of ground states already proved for the scalar NLS. Here the ke…
On nonlinear profile decompositions and scattering for a NLS-ODE model
Scipio Cuccagna, Masaya Maeda
In this paper, we consider a Hamiltonian system combining a nonlinear Schr\" odinger equation (NLS) and an ordinary differential equation (ODE). This system is a simplified model o…
On small energy stabilization in the NLKG with a trapping potential
Scipio Cuccagna, Masaya Maeda, Tuoc V. Phan
We consider a nonlinear Klein Gordon equation (NLKG) with short range potential with eigenvalues and show that in the contest of complex valued solutions the small standing waves a…
On orbital instability of spectrally stable vortices of the NLS in the plane
Scipio Cuccagna, Masaya Maeda
We explain how spectrally stable vortices of the Nonlinear Schrödinger Equation in the plane can be orbitally unstable. This relates to the nonlinear Fermi golden rule, a mechanism…
On asymptotic stability of N-solitons of the defocusing nonlinear Schrodinger equation
Scipio Cuccagna, Robert Jenkins
We consider the Cauchy problem for the Gross-Pitaevskii (GP) equation. Using the DBAR generalization of the nonlinear steepest descent method of Deift and Zhou we derive the leadin…
On stabilization of small solutions in the nonlinear Dirac equation with a trapping potential
Scipio Cuccagna, Mirko Tarulli
We consider a Dirac operator with short range potential and with eigenvalues. We add a nonlinear term and we show that the small standing waves of the corresponding nonlinear Dirac…