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Nakao Hayashi

Nakao Hayashi

D-Index & Metrics

Mathematics

D-Index
38
Citations
5690
World Ranking
2362
National Ranking
38

Research.com Recognitions

  • 2011 - SPIE Fellow

Overview

Nakao Hayashi is a researcher affiliated with Waseda University in Japan, specializing in mathematical physics and applied mathematics. Their work primarily focuses on nonlinear Schrödinger equations and related boundary value problems, contributing to the understanding of complex differential equations and nonlinear wave phenomena.

The researcher has published extensively in fields including Mathematics and Physics and Astronomy. Their subfields of study encompass Mathematical Physics, Statistical and Nonlinear Physics, Applied Mathematics, Computational Theory and Mathematics, and Control and Systems Engineering. Key topics covered include advanced mathematical physics problems, nonlinear waves and solitons, nonlinear photonic systems, spectral theory in mathematical physics, differential equations and boundary problems, and advanced mathematical modeling in engineering.

Hayashi's frequent publication venues reflect the interdisciplinary nature of their work. These include Partial Differential Equations and Applications, Journal of Evolution Equations, Nonlinear Analysis, Journal of Pseudo-Differential Operators and Applications, and Differential and Integral Equations.

Hayashi has collaborated with several researchers, notably Pavel I. Naumkin, with whom they have co-authored 23 papers. Other frequent co-authors include Takayoshi Ogawa, Elena I. Kaikina, Jesus A. Mendez-Navarro, and Takuya Sato.

Their recent significant papers include:

  • Inhomogeneous Neumann-boundary value problem for nonlinear Schrödinger equations in the upper half-space (2021), published in Differential and Integral Equations
  • Critical exponent for global existence of solutions to the Schrödinger equation with a nonlinear boundary condition (2023), published in Nonlinear Analysis
  • Higher-order nonlinear Schrödinger equation in 2D case (2020), published in Tohoku Mathematical Journal
  • Asymptotics for the fractional nonlinear Schrödinger equation with 2 < α < 5/2 (2022), published in Journal of Pseudo-Differential Operators and Applications
  • Dirichlet-boundary value problem for one dimensional nonlinear Schrödinger equations with large initial and boundary data (2020), published in Nonlinear Differential Equations and Applications NoDEA

In recognition of their contributions, Nakao Hayashi was awarded the distinction of SPIE Fellow in 2011.

Best Publications

  • Asymptotics for large time of solutions to the nonlinear Schrödinger and Hartree equations

    Nakao Hayashi;Pavel I. Naumkin

  • Global Existence of Small Solutions to a Relativistic Nonlinear Schrödinger Equation

    Anne De Bouard;Nakao Hayashi;Jean Claude Saut

  • On the derivative nonlinear Schro¨dinger equation

    Nakao Hayashi;Tohru Ozawa

  • Finite energy solutions of nonlinear Schro¨dinger equations of derivative type

    Nakao Hayashi;Tohru Ozawa

  • Remarks on nonlinear Schrödinger equations in one space dimension

    Nakao Hayashi;Tohru Ozawa;Tohru Ozawa;Tohru Ozawa;J. L. Bona

  • On the global strong solutions of coupled Klein-Gordon-Schrödinger equations

    Nakao Hayashi;Wolf von Wahl

  • Damped wave equation with super critical nonlinearities

    Nakao Hayashi;Elena I. Kaikina;Pavel I. Naumkin

  • On solutions of the initial value problem for the nonlinear Schrödinger equations

    Nakao Hayashi;Kuniaki Nakamitsu;Masayoshi Tsutsumi

  • The initial value problem for the cubic nonlinear Klein–Gordon equation

    Nakao Hayashi;Pavel I. Naumkin

  • On a system of nonlinear Schrödinger equations with quadratic interaction

    Nakao Hayashi;Tohru Ozawa;Kazunaga Tanaka

  • Scattering theory in the weighted $L^2 (\mathbb {R}^n)$ spaces for some Schrödinger equations

    Nakao Hayashi;Tohru Ozawa

  • Scattering theory for Hartree type equations

    Nakao Hayashi;Yoshio Tsutsumi

  • On solutions of the initial value problem for the nonlinear Schrödinger equations in one space dimension

    Nakao Hayashi;Kuniaki Nakamitsu;Masayoshi Tsutsumi

  • Analyticity and smoothing effect for the Schrödinger equation

    Nakao Hayashi;Saburou Saitoh

  • Large time behavior of solutions for the modified Korteweg-de Vries equation

    Nakao Hayashi;Pavel I. Naumkin

  • Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations

    Anne De Bouard;Nakao Hayashi;Keiichi Kato

  • Nonlinear Theory of Pseudodifferential Equations on a Half-Line

    Elena Kaikina;Nakao Hayashi

  • Smoothing effect for some Schrödinger equations

    Nakao Hayashi;Tohru Ozawa

  • Analyticity of solutions of the Korteweg-De Vries equation

    Nakao Hayashi

  • Damped wave equation with a critical nonlinearity

    Nakao Hayashi;Elena I. Kaikina;Pavel I. Naumkin

  • Global strong solutions of coupled Klein-Gordon-Schrödinger equations

    N. Hayashi

Frequent Co-Authors

Tohru Ozawa
Tohru Ozawa Waseda University
Jean-Claude Saut
Jean-Claude Saut University of Paris-Saclay
Masahiro Yamamoto
Masahiro Yamamoto University of Tokyo
Kazunaga Tanaka
Kazunaga Tanaka Waseda University

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