21 citations · 93 across the 32 of their papers we have counts for
25 papers · 1 filter
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…
Center stable manifold for ground states of nonlinear Schrödinger equations with internal modes
Masaya Maeda, Yohei Yamazaki
We study the dynamics of solutions of nonlinear Schrödinger equation near unstable ground states. The existence of the local center stable manifold around ground states and the asy…
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…
A remark on uniform Strichartz estimate for quantum walks on 1D lattice
Takumi Aso, Masaya Maeda
In this short note, we study quantum walks (QWs) on one dimensional lattice . Following Hong-Yang, we prove Strichartz estimates for QWs independent of the lattice wid…
Asymptotic stability of soliton for discrete nonlinear Schrödinger equation on one-dimensional lattice
Masaya Maeda, Masafumi Yoneda
In this paper we give a simple and short proof of asymptotic stability of soliton for discrete nonlinear Schrödinger equation near anti-continuous limit. Our novel insight is that…
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…
Stabilization of small solutions of discrete NLS with potential having two eigenvalues
Masaya Maeda
We study the long time behavior of small (in ) solutions of discrete nonlinear Schrödinger equations with potential. In particular, we are interested in the case that the corr…
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 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…
A note on small periodic solutions of discrete nonlinear Klein-Gordon equations
Masaya Maeda
In this note, we consider discrete nonlinear Klein-Gordon equations with potential. By the pioneering work of Sigal, it is known that for the "continuous" nonlinear Klein-Gordon eq…
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…
Existence and asymptotic stability of quasi-periodic solution of discrete NLS with potential in
Masaya Maeda
We prove the existence of a 2-parameter family of small quasi-periodic in time solutions of discrete nonlinear Schrödinger equation (DNLS). We further show that all small solutions…
On weak interaction between a ground state and a trapping potential
Scipio Cuccagna, Masaya Maeda
We study the interaction of a ground state with a class of trapping potentials. We track the precise asymptotic behavior of the solution if the interaction is weak, either because…
On weak interaction between a ground state and a non-trapping potential
Scipio Cuccagna, Masaya Maeda
We show that ground states of the NLS moving at nonzero speed are asymptotically stable if they either stay far from the potential, or the potential is small, or the ground state h…
On small energy stabilization in the NLS with a trapping potential
Scipio Cuccagna, Masaya Maeda
We describe the asymptotic behavior of small energy solutions of an NLS with a trapping potential. In particular we generalize work of Soffer and Weinstein, and of Tsai et. al. The…
An example of stable excited state on nonlinear Schrödinger equation with nonlocal nonlinearity
Masaya Maeda, Satoshi Masaki
In this article, we consider nonlinear Schrödinger equation with nonlocal nonlinearity which is a generalized model of the Schrödinger-Poisson system (Schrödinger-Newton equations)…
Construction of blow-up solutions for Zakharov system on
Nobu Kishimoto, Masaya Maeda
We consider the Zakharov system in two space dimension with periodic boundary condition. We prove the existence of finite time blow-up solutions. Further, we show there exists no m…