11 citations · 12 across the 3 of their papers we have counts for
10 papers
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 \…