35 citations · 161 across the 28 of their papers we have counts for
30 papers
Scattering of non-radial solutions for the fourth-order Schrödinger equation with -critical and supercritical nonlinearity
Takahisa Inui, Koichi Komada, Kuranosuke Nishimura
We consider the focusing nonlinear fourth-order Schrödinger equation \begin{equation*} i \partial_t u + μΔu - Δ^2 u = - |u|^{p-1} u, \ \ \ (t,x) \in \mathbb{R} \times \mathbb{R}^d,…
Scattering for the quadratic NLS system in without mass resonance or radial symmetry
Takahisa Inui, Kuranosuke Nishimura
We consider the quadratic NLS system \begin{equation*} \begin{cases} i\partial_tu+Δu=v\bar{u},\newline i\partial_tv+κΔv=u^2, \end{cases} \qquad (t,x)\in\mathbb{R}\times\mathbb{R}^5…
Asymptotic behavior for the damped Schrödinger equation with nonlinear dissipation
Takahisa Inui, Shun Takizawa
We consider large time asymptotics of solutions to the damped Schrödinger equation with the nonlinear dissipation in the mass-subcritical case. We prove that the optimal -deca…
Existence of small semi-vortex solutions for the cubic nonlinear Schrödinger system with Rashba type Spin-Orbit coupling on
Takahisa Inui
We consider the cubic nonlinear Schrödinger system with Rashba type Spin-Orbit Coupling (SOC) on . The system describes SO-coupled spinor BEC in physics. In the liter…
Existence of solutions to the semilinear damped wave equation with non- slowly decaying data : polynomial nonlinearity case
Masahiro Ikeda, Takahisa Inui, Yuta Wakasugi
We study the Cauchy problem of the semilinear damped wave equation with polynomial nonlinearity, and establish the local and global existence of the solution for slowly decaying in…
Global dynamics below a threshold for the nonlinear Schrödinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph
Masaru Hamano, Masahiro Ikeda, Takahisa Inui +1
We consider the nonlinear Schrödinger equations on the star graph with the Kirchhoff boundary and the repulsive Dirac delta boundary at the origin. In the present paper, we show th…
Threshold even solutions to the nonlinear Schrödinger equation with delta potential at high frequencies
Stephen Gustafson, Takahisa Inui
We consider the nonlinear Schrödinger equation with a repulsive Dirac delta potential in one dimensional Euclidean space. We classify the global dynamics of even solutions with the…
Blow-up or Grow-up for the threshold solutions to the nonlinear Schrödinger equation
Stephen Gustafson, Takahisa Inui
We consider the nonlinear Schrödinger equation with -supercritical and -subcritical power type nonlinearity. Duyckaerts and Roudenko and Campos, Farah, and Roudenko s…
Traveling waves for a nonlinear Schrödinger system with quadratic interaction
Noriyoshi Fukaya, Masayuki Hayashi, Takahisa Inui
We study traveling wave solutions for a nonlinear Schrödinger system with quadratic interaction. For the non mass resonance case, the system has no Galilean symmetry, which is of p…
Threshold odd solutions to the nonlinear Schrödinger equation in one dimension
Stephen Gustafson, Takahisa Inui
We consider odd solutions to the Schrödinger equation with the -supercritical power type nonlinearity in one dimensional Euclidean space. It is known that the odd solution sca…
Non relativistic and ultra relativistic limits in 2d stochastic nonlinear damped Klein-Gordon equation
Reika Fukuizumi, Masato Hoshino, Takahisa Inui
We study the non relativistic and ultra relativistic limits in the two-dimensional nonlinear damped Klein-Gordon equation driven by a space-time white noise on the torus. In order…
Threshold scattering for the focusing NLS with a repulsive Dirac delta potential
Alex H. Ardila, Takahisa Inui
We establish the scattering of solutions to the focusing mass supercritical nonlinear Schrödinger equation with a repulsive Dirac delta potential \[ i\partial_{t}u+\partial^{2}_{x}…
Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation
Takahisa Inui, Shuji Machihara
We consider a singular limit problem from the damped wave equation with a power type nonlinearity to the corresponding heat equation. We call our singular limit problem non-delay l…
Modified scattering for inhomogeneous nonlinear Schrödinger equations with and without inverse-square potential
Kazuki Aoki, Takahisa Inui, Hayato Miyazaki +2
We consider the final state problem for the inhomogeneous nonlinear Schrödinger equation with a critical long-range nonlinearity. Given a prescribed asymptotic profile, which has a…
Asymptotic behavior for the long-range nonlinear Schrödinger equation on star graph with the Kirchhoff boundary condition
Kazuki Aoki, Takahisa Inui, Hayato Miyazaki +2
We consider the cubic nonlinear Schrödinger equation on the star graph with the Kirchhoff boundary condition. We prove modified scattering for the final state problem and the initi…
Remarks on asymptotic order for the linear wave equation with the scale-invariant damping and mass with -data
Takahisa Inui, Haruya Mizutani
In the present paper, we consider the linear wave equation with the scale-invariant damping and mass. It is known that the global behavior of the solution depends on the size of th…
Scattering and asymptotic order for the wave equations with the scale-invariant damping and mass
Takahisa Inui, Haruya Mizutani
We consider the linear wave equation with the time-dependent scale-invariant damping and mass. We also treat the corresponding equation with the energy critical nonlinearity. Our a…
Failure of scattering to standing waves for a Schrödinger equation with long-range nonlinearity on star graph
Kazuki Aoki, Takahisa Inui, Haruya Mizutani
We consider the Schrödinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet, , o…
The Strichartz estimates for the damped wave equation and the behavior of solutions for the energy critical nonlinear equation
Takahisa Inui
For the linear damped wave equation (DW), the - type estimates have been well studied. Recently, Watanabe showed the Strichartz estimates for DW when . In the pres…
Scattering for the quadratic nonlinear Schrödinger system in without mass-resonance condition
Masaru Hamano, Takahisa Inui, Kuranosuke Nishimura
We consider the quadratic nonlinear Schrödinger system (NLS system) \begin{align*}\begin{cases} i\partial_t u + Δu = v \overline{u}, \\ i\partial_t v+κΔv = u^2, \end{cases} \text{…
Endpoint Strichartz estimate for the damped wave equation and its application
Takahisa Inui, Yuta Wakasugi
Recently, the Strichartz estimates for the damped wave equation was obtained by the first author except for the wave endpoint case. In the present paper, we give the Strichartz est…
Scattering for the one-dimensional Klein-Gordon equation with exponential nonlinearity
Masahiro Ikeda, Takahisa Inui, Mamoru Okamoto
We consider the asymptotic behavior of solutions to the Cauchy problem for the defocusing nonlinear Klein-Gordon equation (NLKG) with exponential nonlinearity in the one spatial di…
Scattering for a mass critical NLS system below the ground state with and without mass-resonance condition
Takahisa Inui, Nobu Kishimoto, Kuranosuke Nishimura
We consider a mass-critical system of nonlinear Schödinger equations \begin{align*} \begin{cases} i\partial_t u +Δu =\bar{u}v,\\ i\partial_t v +κΔv =u^2, \end{cases} (t,x)\in \math…
Blow-up of the radially symmetric solutions for the quadratic nonlinear Schrödinger system without mass-resonance
Takahisa Inui, Nobu Kishimoto, Kuranosuke Nishimura
We consider the quadratic nonlinear Schrödinger system \begin{align*} \begin{cases} i\partial_t u +Δu =v \overline{u},\\ i\partial_t v +κΔv =u^2, \end{cases} \text{ on } I \times \…