16 citations · 65 across the 21 of their papers we have counts for
23 papers
Scattering problem for Zakharov-Kuznetsov equation in three space dimensions
Jun-ichi Segata
This paper is a continuation of our previous study arXiv:2507.01288 on the scattering problem for the Zakharov-Kuznetsov equation (ZK). When the space dimension is three, we constr…
Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions
Jun-ichi Segata
In this paper, we study long time behavior of solution to the two dimensional Zakharov-Kuznetsov equation in the framework of the final state problem. We construct a small global s…
Non-polynomial conserved quantities for ODE systems and its application to the long-time behavior of solutions to cubic NLS systems
Satoshi Masaki, Jun-ichi Segata, Kota Uriya
In this paper, we investigate the asymptotic behavior of small solutions to the initial value problem for a system of cubic nonlinear Schrodinger equations (NLS) in one spatial dim…
Scattering problem for the generalized Korteweg-de Vries equation
Satoshi Masaki, Jun-ichi Segata
In this paper we study the scattering problem for the initial value problem of the generalized Korteweg-de Vries (gKdV) equation. The purpose of this paper is to achieve two primar…
Polynomial deceleration for a system of cubic nonlinear Schrödinger equations in one space dimension
Naoyasu Kita, Satoshi Masaki, Jun-ichi Segata +1
In this paper, we consider the initial value problem of a specific system of cubic nonlinear Schrödinger equations. Our aim of this research is to specify the asymptotic profile of…
Global dynamics below excited solitons for the non-radial NLS with potential
Satoshi Masaki, Jason Murphy, Jun-ichi Segata
We consider the global dynamics of solutions to the cubic nonlinear Schrödinger equation in the presence of an external potential, in the setting in which the equation admits…
Asymptotic behavior in time of solution to system of cubic nonlinear Schr"odinger equations in one space dimension
Satoshi Masaki, Jun-ichi Segata, Kota Uriya
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Schr"odinger equations in one space dimension. It turns out that for a…
On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension
Satoshi Masaki, Jun-ichi Segata, Kota Uriya
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems…
Asymptotic stability of solitary waves for the NLS with an attractive delta potential
Satoshi Masaki, Jason Murphy, Jun-ichi Segata
We consider the one-dimensional nonlinear Schrödinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family o…
Long range scattering for the nonlinear Schr"odinger equation with higher order anisotropic dispersion in two dimensions
Jean-Claude Saut, Jun-ichi Segata
This paper is a continuation of our previous study on the long time behavior of solution to the nonlinear Schr"odinger equation with higher order anisotropic dispersion (4NLS). We…
Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions
Satoshi Masaki, Jun-ichi Segata, Kota Uriya
In this paper, we study large time behavior of complex-valued solutions to nonlinear Klein-Gordon equation with a gauge invariant quadratic nonlinearity in two spatial dimensions.…
Stability of small solitary waves for the 1 NLS with an attractive delta potential
Satoshi Masaki, Jason Murphy, Jun-ichi Segata
We consider the initial-value problem for the one-dimensional nonlinear Schrödinger equation in the presence of an attractive delta potential. We show that for sufficiently small i…
Asymptotic behavior in time of solution to the nonlinear Schr"odinger equation with higher order anisotropic dispersion
Jean-Claude Saut, Jun-ichi Segata
We consider the asymptotic behavior in time of solutions to the nonlinear Schr"odinger equation with fourth order anisotropic dispersion (4NLS) which describes the propagation of u…
Modified scattering for the cubic NLS with a repulsive delta potential
Satoshi Masaki, Jason Murphy, Jun-ichi Segata
We consider the initial-value problem for the cubic nonlinear Schrödinger equation with a repulsive delta potential. We prove that small initial data in a weighted Sobolev spa…
Refinement of Strichartz estimate for Airy equation in non-diagonal case and its application
Satoshi Masaki, Jun-ichi Segata
In this paper, we give an improvement of the Strichartz estimate for Airy equation in the non-diagonal case. As an application, we prove the small data scattering and existence of…
Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions
Satoshi Masaki, Jun-ichi Segata
In this paper, we consider the final state problem for the nonlinear Klein-Gordon equation (NLKG) with a critical nonlinearity in three space dimensions. We prove that for a given…
Modified scattering for the quadratic nonlinear Klein-Gordon equation in two dimensions
Satoshi Masaki, Jun-ichi Segata
In this paper, we consider the long time behavior of solution to the quadratic gauge invariant nonlinear Klein-Gordon equation (NLKG) in two space dimensions. For a given asymptoti…
The fourth order nonlinear Schrodinger limit for quantum Zakharov system
Yung-Fu Fang, Chi-Kun Lin, Jun-ichi Segata
This paper is concerned with the quantum Zakharov system. We prove that when the ionic speed of sound goes to infinity, the solution to the fourth order Schrodinger part of the qua…
Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation
Satoshi Masaki, Jun-ichi Segata
In this article, we prove existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg-de Vries (gKdV) equation in the scale…
On well-posedness of generalized Korteweg-de Vries equation in scale critical ^L^r space
Satoshi Masaki, Jun-ichi Segata
The purpose of this paper is to study local and global well-posedness of initial value problem for generalized Korteweg-de Vries (gKdV) equation in ^L^r. We show (large data) local…
Propagation of regularity and persistence of decay for fifth order dispersive models
Jun-ichi Segata, Derek L. Smith
This paper considers the initial value problem for a class of fifth order dispersive models containing the fifth order KdV equation $$\partial_tu - \partial_x^5u - 30u^2\partial_xu…
Final state problem for the cubic nonlinear Schr"odinger equation with repulsive delta potential
Jun-ichi Segata
We consider the asymptotic behavior in time of solutions to the cubic nonlinear Schr"odinger equation with repulsive delta potential (delta-NLS). We shall prove that for a given as…
Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrodinger type equation on torus
Jun-ichi Segata
We consider the time local and global well-posedness for the fourth order nonlinear Schrodinger type equation (4NLS) on the torus. The nonlinear term of (4NLS) contains the derivat…