47 citations · 162 across the 11 of their papers we have counts for
12 papers
Instability theory of stationary solutions for nonlinear Schrödinger equations
Noriyoshi Fukaya, Masayuki Hayashi
We study the orbital instability of algebraically decaying stationary solutions of nonlinear Schrödinger equations in dimensions , taking competing double-power nonlineariti…
Instability of stationary solutions for double power nonlinear Schrödinger equations in one dimension
Noriyoshi Fukaya, Masayuki Hayashi
We consider a double power nonlinear Schrödinger equation which possesses the algebraically decaying stationary solution as well as exponentially decaying standing waves $e^{…
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…
Sharp thresholds for stability and instability of standing waves in a double power nonlinear Schrödinger equation
Masayuki Hayashi
We study the stability/instability of standing waves for the one dimensional nonlinear Schrödinger equation with double power nonlinearities: \begin{align*} &i\partial_t u +\partia…
Instability of degenerate solitons for nonlinear Schrödinger equations with derivative
Noriyoshi Fukaya, Masayuki Hayashi
We consider the following nonlinear Schrödinger equation with derivative: \begin{equation} iu_t =-u_{xx} -i |u|^{2}u_x -b|u|^4u , \quad (t,x) \in \mathbb{R}\times\mathbb{R}, \ b \i…
Potential well theory for the derivative nonlinear Schrödinger equation
Masayuki Hayashi
We consider the following nonlinear Schrödinger equation of derivative type: \begin{equation}i \partial_t u + \partial_x^2 u +i |u|^{2} \partial_x u +b|u|^4u=0 , \quad (t,x) \in \m…
Stability of algebraic solitons for nonlinear Schrödinger equations of derivative type: variational approach
Masayuki Hayashi
We consider the following nonlinear Schrödinger equation of derivative type: \begin{equation} i \partial_t u + \partial_x^2 u +i |u|^{2} \partial_x u +b|u|^4u=0 , \quad (t,x) \in \…
Instability of algebraic standing waves for nonlinear Schrödinger equations with double power nonlinearities
Noriyoshi Fukaya, Masayuki Hayashi
We consider a nonlinear Schrödinger equation with double power nonlinearity \begin{align*} i\partial_t u+Δu-|u|^{p-1}u+|u|^{q-1}u=0,\quad (t,x)\in\mathbb{R}\times\mathbb{R}^N, \end…
Long-period limit of exact periodic traveling wave solutions for the derivative nonlinear Schrödinger equation
Masayuki Hayashi
We study the periodic traveling wave solutions of the derivative nonlinear Schrödinger equation (DNLS). It is known that DNLS has two types of solitons on the whole line; one has e…
A note on the nonlinear Schrödinger equation in a general domain
Masayuki Hayashi
We consider the Cauchy problem for nonlinear Schrödinger equations in a general domain . Construction of solutions has been only done by classical compactness…
A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation
Noriyoshi Fukaya, Masayuki Hayashi, Takahisa Inui
We give a sufficient condition for global existence of the solutions to a generalized derivative nonlinear Schrödinger equation (gDNLS) by a variational argument. The variational a…
Well-posedness for a generalized derivative nonlinear Schrödinger equation
Masayuki Hayashi, Tohru Ozawa
We study the Cauchy problem for a generalized derivative nonlinear Schrödinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the…