21 citations · 93 across the 32 of their papers we have counts for
33 papers
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…
Asymptotic stability of small bound state of nonlinear quantum walks
Masaya Maeda
In this paper, we study the long time behavior of nonlinear quantum walks when the initial data is small in . In particular, we study the case where the linear part of the qua…
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.
Absence of singular continuous spectra and embedded eigenvalues for one dimensional quantum walks with general long-range coins
Masaya Maeda, Akito Suzuki, Kazuyuki Wada
This paper is a continuation of the paper \cite{W} by the third author, which studied quantum walks with special long-range perturbations of the coin operator. In this paper, we co…
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…
Continuous limits of linear and nonlinear quantum walks
Masaya Maeda, Akito Suzuki
In this paper, we consider the continuous limit of a nonlinear quantum walk (NLQW) that incorporates a linear quantum walk as a special case. In particular, we rigorously prove tha…
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…
Dispersive estimates for quantum walks on 1D lattice
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2
We consider quantum walks with position dependent coin on 1D lattice . The dispersive estimate is shown…
Dynamics of solitons for nonlinear quantum walks
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2
We present some numerical results for nonlinear quantum walks (NLQWs) studied by the authors analytically \cite{MSSSS18DCDS, MSSSS18QIP}. It was shown that if the nonlinearity is w…
Scattering and inverse scattering for nonlinear quantum walks
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2
We study large time behavior of quantum walks (QWs) with self-dependent (nonlinear) coin. In particular, we show scattering and derive the reproducing formula for inverse scatterin…
Weak limit theorem for a nonlinear quantum walk
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2
This paper continues the study of large time behavior of a nonlinear quantum walk begun in arXiv:1801.03214. In this paper, we provide a weak limit theorem for the distribution of…
On nonlinear scattering for quantum walks
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2
We study large time behavior of quantum walks (QW) with self-dependent coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak…
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…