25 citations · 107 across the 17 of their papers we have counts for
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On solitary wave solutions with two-frequency parameters to the three-component system of quadratic nonlinear Schrödinger equations
Hiroyuki Hirayama, Masahiro Ikeda
In the present paper, we consider the Cauchy problem of a system of three nonlinear Schrödinger equations with quadratic nonlinearity. We first prove the existence of ground states…
Well-posedness and ill-posedness for a system of periodic quadratic derivative nonlinear Schrödinger equations
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
We consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma i…
Variational problems for the system of nonlinear Schrödinger equations with derivative nonlinearities
Hiroyuki Hirayama, Masahiro Ikeda
We consider the Cauchy problem of the system of nonlinear Schrödinger equations with derivative nonlinearlity. This system was introduced by Colin-Colin (2004) as a model of laser-…
Sharp well-posedness for the Cauchy problem of the two dimensional quadratic nonlinear Schrödinger equation with angular regularity
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
This paper is concerned with the Cauchy problem of the quadratic nonlinear Schrödinger equation in with the nonlinearity where $η\in \math…
Large time behavior and optimal decay estimate for solutions to the generalized Kadomtsev--Petviashvili--Burgers equation in 2D
Ikki Fukuda, Hiroyuki Hirayama
We consider the Cauchy problem for the generalized Kadomtsev--Petviashvili--Burgers equation in 2D. This is one of the nonlinear dispersive-dissipative type equations, which has a…
Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations in almost critical spaces
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
In this paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations introduced by Colin and Colin (2004). We determine an almost opt…
Well-posedness for the fourth-order Schrödinger equation with third order derivative nonlinearities
Hiroyuki Hirayama, Masahiro Ikeda, Tomoyuki Tanaka
We study the Cauchy problem to the semilinear fourth-order Schrödinger equations: \begin{equation}\label{0-1}\tag{4NLS} \begin{cases} i\partial_t u+\partial_x^4u=G\left(\left\{\par…
Well-posedness for KdV-type equations with quadratic nonlinearity
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
We consider the Cauchy problem of the KdV-type equation \[ \partial_t u + \frac{1}{3} \partial_x^3 u = c_1 u \partial_x^2u + c_2 (\partial_x u)^2, \quad u(0)=u_0. \] Pilod (2008) s…
Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with radial initial data
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations. This system was introduced by M. Colin and T. Colin (200…
Local and global well-posedness for the 2D Zakharov-Kuznetsov-Burgers equation in low regularity Sobolev space
Hiroyuki Hirayama
In the present paper, we consider the Cauchy problem of the 2D Zakharov-Kuznetsov-Burgers (ZKB) equation, which has the dissipative term . This is known that the 2D…
Sharp bilinear estimates and its application to a system of quadratic derivative nonlinear Schrödinger equations
Hiroyuki Hirayama, Shinya Kinoshita
In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations for the spatial dimension and . This system was…
Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity
Hiroyuki Hirayama, Mamoru Okamoto
We consider the Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity on , , with…
Random data Cauchy theory for the fourth order nonlinear Schrödinger equation with cubic nonlinearity
Hiroyuki Hirayama, Mamoru Okamoto
We consider the Cauchy problem for the fourth order nonlinear Schrödinger equation with derivative nonlinearity on ,…
Well-posedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity
Hiroyuki Hirayama, Mamoru Okamoto
In the present paper, we consider the Cauchy problem of fourth order nonlinear Schrödinger type equations with a derivative nonlinearity. In one dimensional case, we prove that the…
Well-posedness and scattering for nonlinear Schrödinger equations with a derivative nonlinearity at the scaling critical regularity
Hiroyuki Hirayama
In the present paper, we consider the Cauchy problem of nonlinear Schrödinger equations with a derivative nonlinearity which depends only on . The well-posedness of the eq…
Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with low regularity periodic initial data
Hiroyuki Hirayama
We consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma i…
Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data
Hiroyuki Hirayama
In the present paper, we consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin (2004) as a m…