13 citations · 77 across the 21 of their papers we have counts for
11 papers · 1 filter
On Schrödinger equation with square and inverse-square potentials
Atsuhide Ishida, Masaki Kawamoto
In this paper, we study the linear and nonlinear Schrödinger equations with a time-decaying harmonic oscillator and inverse-square potential. This model retains a form of scale inv…
Modified scattering for nonlinear Schrödinger equations with long-range potentials
Masaki Kawamoto, Haruya Mizutani
We study the final state problem for the nonlinear Schrödinger equation with a critical long-range nonlinearity and a long-range linear potential. Given a prescribed asymptotic pro…
Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials
Masaki Kawamoto, Hayato Miyazaki
This paper is concerned with the final state problem for the homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potential. The nonlinearity has the critica…
Asymptotic behavior of solutions to a dissipative nonlinear Schrödinger equation with time dependent harmonic potentials
Masaki Kawamoto, Takuya Sato
We consider the Cauchy problem of a dissipative nonlinear Schrödinger equation with a time dependent harmonic potential. We find a critical situation that the -norm of dissipa…
-stableness for solution to linearized KdV equation
Masaki Kawamoto, Hisashi Morioka
The linearized Korteweg-De Vries equation can be written as a Hamilton-like system. However, the Hamilton energy depends on the time, and is a nonsymmetric operator on $L^2({\bf R}…
Final state problem for nonlinear Schrödinger equations with time-decaying harmonic oscillators
Masaki Kawamoto
We consider the final-state problem for the nonlinear Schrödinger equations (NLS) with a suitable time-decaying harmonic oscillator. In this equation, the power of nonlinearity $|u…
Asymptotic behavior for nonlinear Schrödinger equations with critical time-decaying harmonic potential
Masaki Kawamoto
Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of the nonlinearity between the short and the long range. In the non-c…
Singularity for Solutions of Linearized KdV Equations
Keiichi Kato, Masaki Kawamoto, Koichiro Nanbu
We investigate the time propagation of singularity of a solution to linearized KdV equation by using the characterization of wave front sets with using to the wave packet transform…
High-Energy Smoothing Estimates for Selfadjoint Operators
Masaki Kawamoto
We prove the limiting absorption principle on the non-compact interval , on which the uniformly positive Mourre estimate holds. We reveal that such a result yields so-called smo…
Strichartz estimates for Schrödinger operators with square potential with time-dependent coefficients
Masaki Kawamoto
Strichartz estimates for a time-decaying harmonic oscillator were proven with some assumptions of coefficients for the time-decaying harmonic potentials. The main results of this p…
Strichartz estimates for quadratic repulsive potentials
Masaki Kawamoto, Taisuke Yoneyama
Quadratic repulsive potentials accelerate the quantum particle, increasing the velocity of the particle exponentially in ; this phenomenon yields fast decaying di…