Satoshi Masaki
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View article: Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance
Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance Open
In this paper, we consider the nonlinear Schrödinger equation (NLS) with a general homogeneous nonlinearity in dimensions up to three. We assume that the degree (i.e., power) of the nonlinearity is such that the equation is mass-subcritica…
View article: Non-polynomial conserved quantities for ODE systems and its application to the long-time behavior of solutions to cubic NLS systems
Non-polynomial conserved quantities for ODE systems and its application to the long-time behavior of solutions to cubic NLS systems Open
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 dimension. We identify a new class of NLS systems for which th…
View article: Global existence and large-time behavior of solutions to cubic nonlinear Schrödinger systems without coercive conserved quantity
Global existence and large-time behavior of solutions to cubic nonlinear Schrödinger systems without coercive conserved quantity Open
In this article, we investigate the large-time behavior of small solutions to a system of one-dimensional cubic nonlinear Schrödinger equations with two components. In previous studies, a structural condition on the nonlinearity has been e…
View article: Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance
Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance Open
In this paper, we consider the nonlinear Schrödinger equation (NLS) with a general homogeneous nonlinearity in dimensions up to three. We assume that the degree (i.e., power) of the nonlinearity is such that the equation is mass-subcritica…
View article: Scattering problem for the generalized Korteweg-de Vries equation
Scattering problem for the generalized Korteweg-de Vries equation Open
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 primary goals. Firstly, we show small data scattering for (gKdV) …
View article: Scattering for the focusing, $ L^2 $-supercritical fourth-order NLS in one dimension
Scattering for the focusing, $ L^2 $-supercritical fourth-order NLS in one dimension Open
In this paper, we consider the fourth-order Schrödinger equations with focusing, $ L^2 $-supercritical nonlinearity in one dimension. We prove the global existence and scattering of even solutions below the ground state threshold, under th…
View article: Partial classification of the large-time behavior of solutions to cubic nonlinear Schrödinger systems
Partial classification of the large-time behavior of solutions to cubic nonlinear Schrödinger systems Open
In this paper, we study the large-time behavior of small solutions to the standard form of the systems of 1D cubic nonlinear Schrödinger equations consisting of two components and possessing a coercive mass-like conserved quantity. The cub…
View article: Scattering for the Mass-Critical Nonlinear Klein–Gordon Equations in Three and Higher Dimensions
Scattering for the Mass-Critical Nonlinear Klein–Gordon Equations in Three and Higher Dimensions Open
In this paper we consider the mass-critical nonlinear Klein–Gordon equations in three and higher dimensions. We prove the dichotomy between scattering and blow-up below the ground state energy in the focusing case, and the energy scatterin…
View article: Scattering for the focusing, $L^2$-supercritical fourth-order NLS in one dimension
Scattering for the focusing, $L^2$-supercritical fourth-order NLS in one dimension Open
In this paper, we consider the fourth-order Schrödinger equations with focusing, $L^2$-supercritical nonlinearity in one dimension. We prove the global existence and scattering of solutions below the ground state threshold under the evenne…
View article: Scattering below ground states for a class of systems of nonlinear Schrodinger equations
Scattering below ground states for a class of systems of nonlinear Schrodinger equations Open
In this paper, we consider the scattering problem for a class of $N$-coupled systems of the cubic nonlinear Schrödinger equations in three space dimensions. We prove the scattering of solutions that have a mass-energy quantity less than th…
View article: Asymptotic stability of solitary waves for the <inline-formula><tex-math id="M1">$ 1d $</tex-math></inline-formula> NLS with an attractive delta potential
Asymptotic stability of solitary waves for the NLS with an attractive delta potential Open
We consider the one-dimensional nonlinear Schrödinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family of solitary wave solutions in both the focusing and defocusi…
View article: On scalar-type standing-wave solutions to systems of nonlinear Schrödinger equations
On scalar-type standing-wave solutions to systems of nonlinear Schrödinger equations Open
In this article, we study the standing-wave solutions to a class of systems of nonlinear Schrödinger equations. Our target is all the standard forms of the NLS systems, with two unknowns, that have a common linear part and cubic gauge-inva…
View article: Classification of a class of systems of cubic ordinary differential equations
Classification of a class of systems of cubic ordinary differential equations Open
In this article, we consider the classification of the systems of two ordinary differential equations with a complex-valued unknown and gauge-invariant cubic nonlinearities of polynomial type. The class of systems of ODEs arises in the stu…
View article: On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension
On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension Open
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 by studying the quotient set of a suitable subset of system…
View article: Polynomial deceleration for a system of cubic nonlinear Schrödinger equations in one space dimension
Polynomial deceleration for a system of cubic nonlinear Schrödinger equations in one space dimension Open
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 the solution in $L^{\infty}$ as $t \to \infty$. It is then…
View article: Global dynamics below excited solitons for the non-radial NLS with potential
Global dynamics below excited solitons for the non-radial NLS with potential Open
We consider the global dynamics of solutions to the $3d$ cubic nonlinear Schrödinger equation in the presence of an external potential, in the setting in which the equation admits both ground state solitons and excited solitons at small ma…
View article: Asymptotic behavior in time of solution to system of cubic nonlinear Schr"odinger equations in one space dimension
Asymptotic behavior in time of solution to system of cubic nonlinear Schr"odinger equations in one space dimension Open
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 system there exists a small solution of which asymptotic pr…
View article: On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension
On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension Open
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 by studying the quotient set of a suitable subset of system…
View article: A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system
A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system Open
In this paper, we consider the quadratic nonlinear Schrödinger system in three space dimensions. Our aim is to obtain sharp scattering criteria. Because of the mass-subcritical nature, it is difficult to do so in terms of conserved quantit…
View article: Asymptotic stability of solitary waves for the $1d$ NLS with an attractive delta potential
Asymptotic stability of solitary waves for the $1d$ NLS with an attractive delta potential Open
We consider the one-dimensional nonlinear Schrödinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family of solitary wave solutions in both the focusing and defocusi…
View article: Optimal decay rate of solutions for nonlinear Klein-Gordon systems of critical type
Optimal decay rate of solutions for nonlinear Klein-Gordon systems of critical type Open
We consider the decay rate of solutions to nonlinear Klein-Gordon systems with a critical type nonlinearity. We will specify the optimal decay rate for a specific class of Klein-Gordon systems containing the dissipative nonlinearities. It …
View article: Refinement of Strichartz estimates for Airy equation and application (Regularity, singularity and long time behavior for partial differential equations with conservation law)
Refinement of Strichartz estimates for Airy equation and application (Regularity, singularity and long time behavior for partial differential equations with conservation law) Open
"Regularity, singularity and long time behavior for partial differential equations with conservation law". June 6-8, 2016. edited by Keiichi Kato, Mishio Kawashita, Masashi Misawa and Takayoshi Ogawa. The papers presented in this volume of…
View article: Scattering for the mass-critical nonlinear Klein-Gordon equations in three and higher dimensions
Scattering for the mass-critical nonlinear Klein-Gordon equations in three and higher dimensions Open
In this paper we consider the real-valued mass-critical nonlinear Klein-Gordon equations in three and higher dimensions. We prove the dichotomy between scattering and blow-up below the ground state energy in the focusing case, and the ener…
View article: Optimal decay rate of solutions for nonlinear Klein-Gordon systems of critical type
Optimal decay rate of solutions for nonlinear Klein-Gordon systems of critical type Open
We consider the decay rate of solutions to nonlinear Klein-Gordon systems with a critical type nonlinearity. We will specify the optimal decay rate for a specific class of Klein-Gordon systems containing the dissipative nonlinearites. It w…
View article: A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system
A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system Open
In this paper, we consider the quadratic nonlinear Schrödinger system in three space dimensions. Our aim is to obtain sharp scattering criteria. Because of the mass-subcritical nature, it is difficult to do so in terms of conserved quantit…
View article: Nonexistence of scattering and modified scattering states for some nonlinear Schrödinger equation with critical homogeneous nonlinearity
Nonexistence of scattering and modified scattering states for some nonlinear Schrödinger equation with critical homogeneous nonlinearity Open
We consider large time behavior of solutions to the nonlinear Schrödinger equation with a homogeneous nonlinearity of the critical order which is not necessarily a polynomial. We treat the case in which the nonlinearity contains non-oscill…
View article: The radial mass-subcritical NLS in negative order Sobolev spaces
The radial mass-subcritical NLS in negative order Sobolev spaces Open
We consider the mass-subcritical NLS in dimensions $d\geq 3$ with radial initial data. In the defocusing case, we prove that any solution that remains bounded in the critical Sobolev space throughout its lifespan must be global and scatter…
View article: Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions
Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions Open
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. To find a possible asymptotic behavior, we consider the fin…
View article: Modified scattering for the quadratic nonlinear Klein–Gordon equation in two dimensions
Modified scattering for the quadratic nonlinear Klein–Gordon equation in two dimensions Open
In this paper, we consider the long time behavior of the solution to the quadratic nonlinear Klein–Gordon equation (NLKG) in two space dimensions: $(\Box +1)u=\lambda |u|u$, $t\in \mathbb {R}$, $x\in \mathbb {R}^{2}$, where $\Box =\partial…
View article: Modified Scattering for the One-Dimensional Cubic NLS with a Repulsive Delta Potential
Modified Scattering for the One-Dimensional Cubic NLS with a Repulsive Delta Potential Open
We consider the initial-value problem for the one-dimensional cubic nonlinear Schrödinger equation with a repulsive delta potential. We prove that small initial data in a weighted Sobolev space lead to global solutions that decay in $L^{\i…