Research

I study well-posedness and large-time behavior of solutions to nonlinear dispersive equations.

Research area

Nonlinear Schrödinger equations

Critical and long-range nonlinearities, non-gauge-invariant structures, time-dependent potentials, and spatial inhomogeneity.

Large-time asymptotics

Scattering, modified scattering, non-scattering, and dissipative time decay through critical exponents and weighted function spaces.

Research output

19 Refereed papers

5 Preprints

5 Proceedings & notes

View talks View researchmap

Refereed papers

2026

Correction to the article “Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance”

Masaki Kawamoto Satoshi Masaki Hayato Miyazaki

Mathematische Annalen, vol. 396, no. 1, Article 20

DOI arXiv
2025

Threshold for the existence of scattering states for nonlinear Schrödinger equations without gauge invariance

Hayato Miyazaki Motohiro Sobajima

Proceedings of the American Mathematical Society, vol. 153, no. 11, pp. 4875–4887

DOI arXiv
2025

Refinement of the L²-decay estimate of solutions to nonlinear Schrödinger equations with attractive-dissipative nonlinearity

Naoyasu Kita Hayato Miyazaki Takuya Sato

Journal of Evolution Equations, vol. 25, Article 66

DOI arXiv
2025

Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance

Masaki Kawamoto Satoshi Masaki Hayato Miyazaki

Mathematische Annalen, vol. 392, no. 1, pp. 1051–1097

DOI arXiv
2025

Modified scattering operator for nonlinear Schrödinger equations with time-decaying harmonic potentials

Masaki Kawamoto Hayato Miyazaki

Nonlinear Analysis, vol. 256, 113778

DOI arXiv
2024

Refined L²-decay estimate of solutions to a system of dissipative nonlinear Schrödinger equations

Naoyasu Kita Hayato Miyazaki Yuji Sagawa Takuya Sato

Journal of Applied Science and Engineering A, vol. 5, no. 1, pp. 18–30

DOI
2024

Global behavior of solutions to generalized Gross-Pitaevskii equation

Satoshi Masaki Hayato Miyazaki

Differential Equations and Dynamical Systems, vol. 32, pp. 743–761

DOI arXiv
2023

Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials

Masaki Kawamoto Hayato Miyazaki

Journal of Differential Equations, vol. 365, pp. 127–167

DOI arXiv
2022

Asymptotic behavior for the long-range nonlinear Schrödinger equation on the star graph with the Kirchhoff boundary condition

Kazuki Aoki Takahisa Inui Hayato Miyazaki Haruya Mizutani Kota Uriya

Pure and Applied Analysis, vol. 4, no. 2, pp. 287–311

DOI arXiv
2021

Strong blow-up instability for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations

Hayato Miyazaki

Discrete and Continuous Dynamical Systems, vol. 41, no. 5, pp. 2411–2445

DOI arXiv
2020

Lower bound for the lifespan of solutions to the generalized KdV equation with low-degree of nonlinearity

Hayato Miyazaki

Advanced Studies in Pure Mathematics, vol. 85, pp. 303–313

DOI
2020

Lifespan of solutions to nonlinear Schrödinger equations with general homogeneous nonlinearity of the critical order

Hayato Miyazaki Motohiro Sobajima

Advances in Harmonic Analysis and Partial Differential Equations, pp. 197–207

DOI arXiv
2019

On a class of solutions to the generalized KdV type equation

Felipe Linares Hayato Miyazaki Gustavo Ponce

Communications in Contemporary Mathematics, vol. 21, no. 7, 1850056

DOI arXiv
2019

Long-range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions

Satoshi Masaki Hayato Miyazaki Kota Uriya

Transactions of the American Mathematical Society, vol. 371, no. 11, pp. 7925–7947

DOI arXiv
Local well-posedness for the higher-order generalized KdV type equation with low-degree of nonlinearity

Hayato Miyazaki

to appear in RIMS Kôkyûroku Bessatsu

arXiv
2019

Nonexistence of scattering and modified scattering states for some nonlinear Schrödinger equation with critical homogeneous nonlinearity

Satoshi Masaki Hayato Miyazaki

Differential and Integral Equations, vol. 32, no. 3-4, pp. 121–138

DOI arXiv
2018

Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity

Satoshi Masaki Hayato Miyazaki

SIAM Journal on Mathematical Analysis, vol. 50, no. 3, pp. 3251–3270

DOI arXiv
2017

The derivation of conservation laws for nonlinear Schrödinger equations with power type nonlinearities

Kazumasa Fujiwara Hayato Miyazaki

RIMS Kôkyûroku Bessatsu, vol. B63, pp. 13–21

Handle arXiv (old version)
2014

The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

Hayato Miyazaki

Journal of Mathematical Analysis and Applications, vol. 417, no. 2, pp. 580–600

DOI arXiv

Preprints

2026

Threshold for the existence of scattering states for inhomogeneous nonlinear Schrödinger equations without gauge invariance

Mourad Grira Hayato Miyazaki Slim Tayachi

submitted

arXiv
2026

A Unified Integral Equation Approach to Conservation Laws for Nonlinear Schrödinger Equations

Shuji Machihara Hayato Miyazaki Tohru Ozawa

submitted

arXiv
2026

Large-data L²-decay for attractive-dissipative nonlinear Schrödinger equations without the strong dissipative condition

Naoyasu Kita Hayato Miyazaki Takuya Sato

submitted

arXiv
2025

Remarks on the derivation of the virial identity for nonlinear Schrödinger equations

Tomoyuki Ikeda Shuji Machihara Hayato Miyazaki Tohru Ozawa

submitted

arXiv
2021

Modified scattering for inhomogeneous nonlinear Schrödinger equations with and without inverse-square potential

Kazuki Aoki Takahisa Inui Hayato Miyazaki Haruya Mizutani Kota Uriya

submitted

arXiv

Proceedings and research notes

Non-refereed proceedings, meeting reports, and expository writing.

2025

Kirchhoff境界条件を持つ星グラフ上のSchrödinger作用素について

宮崎隼人

RIMS Kôkyûroku, vol. 2324, pp. 37–53

Link
2023

Improvement of a regularity condition for long-range scattering for NLS with critical homogeneous nonlinearity

Hayato Miyazaki

RIMS Kôkyûroku, vol. 2257, pp. 79–88

Link
2022

パスカル三角形から始まる数学

宮崎隼人

「数学研究」香川県高等学校教育研究会数学部会誌, vol. 66, pp. 1–8
2014

空間遠方で消滅しない境界条件をもつ非線型シュレディンガー方程式のエネルギー解について

宮崎隼人

第36回発展方程式若手セミナー報告集, pp. 175–182
2013

空間遠方で消滅しない初期値をもつ非線形Schrödinger方程式における保存則について

宮崎隼人

第35回発展方程式若手セミナー報告集, pp. 79–84

Research area

Nonlinear Schrödinger equations

Large-time asymptotics

Research output

Refereed papers

Correction to the article “Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance”

Threshold for the existence of scattering states for nonlinear Schrödinger equations without gauge invariance

Refinement of the L²-decay estimate of solutions to nonlinear Schrödinger equations with attractive-dissipative nonlinearity

Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance

Modified scattering operator for nonlinear Schrödinger equations with time-decaying harmonic potentials

Refined L²-decay estimate of solutions to a system of dissipative nonlinear Schrödinger equations

Global behavior of solutions to generalized Gross-Pitaevskii equation

Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials

Asymptotic behavior for the long-range nonlinear Schrödinger equation on the star graph with the Kirchhoff boundary condition

Strong blow-up instability for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations

Lower bound for the lifespan of solutions to the generalized KdV equation with low-degree of nonlinearity

Lifespan of solutions to nonlinear Schrödinger equations with general homogeneous nonlinearity of the critical order

On a class of solutions to the generalized KdV type equation

Long-range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions

Local well-posedness for the higher-order generalized KdV type equation with low-degree of nonlinearity

Nonexistence of scattering and modified scattering states for some nonlinear Schrödinger equation with critical homogeneous nonlinearity

Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity

The derivation of conservation laws for nonlinear Schrödinger equations with power type nonlinearities

The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

Preprints

Threshold for the existence of scattering states for inhomogeneous nonlinear Schrödinger equations without gauge invariance

A Unified Integral Equation Approach to Conservation Laws for Nonlinear Schrödinger Equations

Large-data L²-decay for attractive-dissipative nonlinear Schrödinger equations without the strong dissipative condition

Remarks on the derivation of the virial identity for nonlinear Schrödinger equations

Modified scattering for inhomogeneous nonlinear Schrödinger equations with and without inverse-square potential

Proceedings and research notes

Kirchhoff境界条件を持つ星グラフ上のSchrödinger作用素について

Improvement of a regularity condition for long-range scattering for NLS with critical homogeneous nonlinearity

パスカル三角形から始まる数学

空間遠方で消滅しない境界条件をもつ非線型シュレディンガー方程式のエネルギー解について

空間遠方で消滅しない初期値をもつ非線形Schrödinger方程式における保存則について