25 citations · 66 across the 12 of their papers we have counts for
12 papers
Transverse Instability and Bifurcation Analysis of the line soliton for the NLS equation on a Fractured Strip
Hiroaki Kikuchi, Boris Shakarov, Kenta Tomioka
We consider the nonlinear Schrödinger equation on a two-dimensional strip with an attractive interaction and power nonlinearity. We investigate the transverse stability and bif…
Threshold solutions for the 3D focusing cubic-quintic nonlinear Schrodinger equation at low frequencies
Masaru Hamano, Hiroaki Kikuchi, Minami Watanabe
This paper addresses the focusing cubic-quintic nonlinear Schrodinger equation in three space dimensions. Especially, we study the global dynamics of solutions whose energy and mas…
Non-existence of ground states and gap of variational problems for combined power-type nonlinear scalar field equations involving the Sobolev critical exponent in three space dimensions
Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi +1
In this paper, we consider minimization problems related to the combined power-type nonlinear scalar field equations involving the Sobolev critical exponent in three space dimensio…
Pitchfork bifurcation at line solitons for nonlinear Schrödinger equations on the product space
Takafumi Akahori, Yakine Bahri, Slim Ibrahim +1
In this paper, we study the bifurcation problem from a line soliton for a stationary nonlinear Schrödinger equation on the product space . We extend e…
Transverse stability of line soliton and characterization of ground state for wave guide Schrödinger equations
Yakine Bahri, Slim Ibrahim, Hiroaki Kikuchi
In this paper, we study the transverse stability of the line Schrödinger soliton under a full wave guide Schrödinger flow on a cylindrical domain . When t…
Non-uniqueness for an energy-critical heat equation on
Slim Ibrahim, Hiroaki Kikuchi, Kenji Nakanishi +1
We construct a singular solution of a stationary nonlinear Schrödinger equation on with square-exponential nonlinearity having linear behavior around zero. In view o…
Linear instability and nondegeneracy of ground state for combined power-type nonlinear scalar field equations with the Sobolev critical exponent and large frequency parameter
Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi
We consider combined power-type nonlinear scalar field equations with the Sobolev critical exponent. In \cite{AIKN3}, it was shown that if the frequency parameter is sufficiently s…
Remarks on solitary waves and Cauchy problem for a Half-wave-Schrödinger equations
Yakine Bahri, Slim Ibrahim, Hiroaki Kikuchi
In this paper, we study the solitary wave and the Cauchy problem for Half-wave-Schrödinger equations in the plane. First, we show the existence and orbital stability of the ground…
Uniqueness and nondegeneracy of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in their nonlinearities for high frequencies
Takafumi Akahori, Slim Ibrahim, Norihisa Ikoma +2
The study of the uniqueness and nondegeneracy of ground state solutions to semilinear elliptic equations is of great importance because of the resulting energy landscape and its im…
Global dynamics above the ground state energy for the combined power type nonlinear Schrodinger equations with energy critical growth at low frequencies
Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi +1
We consider the nonlinear Schrodinger equations with combined type local interactions with energy critical growth, and we study the solutions slightly above the ground state thresh…
Existence of a ground state and scattering for a nonlinear Schroedinger equation with critical growth
Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi +1
We study the energy-critical focusing nonlinear Schrödinger equation with an energy- subcritical perturbation. We show the existence of a ground state in the four or higher dimensi…
Existence of a ground state and blow-up problem for a nonlinear Schrodinger equation with critical growth
Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi +1
In this paper we show the existence of ground-state solutions for the energy-critical NLS perturbed with subcritical terms when the space dimension . However in dimension t…