191 citations · 510 across the 23 of their papers we have counts for
23 papers
Large-time existence results for the nonlocal NLS around ground state solutions
Hideo Takaoka, Toshihiro Tamaki
This paper discusses about solutions of the nonlocal nonlinear Schrodinger equation. We prove that the solution remains close to the orbit of the soliton for a large-time, if the i…
On the growth of Sobolev norm for the cubic NLS on two dimensional product space
Hideo Takaoka
We obtain polynomial bounds on the growth in time of Sobolev norm of solutions to the cubic defocusing nonlinear Schrodinger equation on two dimensional product space. We also give…
Bilinear Strichartz estimates for the KdV equation on the torus
Hideo Takaoka
In this paper, we consider the bilinear Strichartz estimates for the periodic KdV equation. We give a concrete counterexample to the false Strichartz estimates for , at…
Remarks on blow-up criteria for the derivative nonlinear Schrodinger equation under the optimal threshold setting
HIdeo Takaoka
We study the Cauchy problem of the mass critical nonlinear Schrodinger equation with derivative with the 4pi mass. One has the global well-posedness in H^1 whenever "the mass is st…
Energy transfer model and large periodic boundary value problem for the quintic nonlinear Schrodinger equations
Hideo Takaoka
We study a dynamics and energy exchanges between a linear oscillator and a nonlinear interaction state for the one dimensional, quintic nonlinear Schrodinger equation. Grebert and…
Energy transfer model for the derivative nonlinear Schrodinger equations on the torus
Hideo Takaoka
We consider the nonlinear derivative Schrodinger equation with a quintic nonlinearity, on the one dimensional torus. We exhibit that the nonlinear dynamic properties consist of fou…