6 papers
A note on the non-existence of small non-trivial compact solutions for Euler-Poisson equation in 1D
Masaya Maeda, Tetsu Mizumachi
In this short note, we prove the non-existence of slow and fast small nontrivial compact solutions for the Euler-Poisson system in D. The proof is based on the virial estimate w…
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 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 Schrödin…
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 equat…
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…