School personnel information




Nonlinear Dispersive Wave Equations

Mail Address

Mail Address




Organization 【 display / non-display

  • 2001.04.01 - , Department of Mathematics, Graduate School of Science, Professor

Education 【 display / non-display

Waseda University Faculty of Science and Engineering  Graduated 1978.03
Waseda University Graduate School, Division of Science and Engineering  Completed 1980.03
Waseda University Graduate School, Division of Science and Engineering  Unfinished 1986.03

Research topics 【 display / non-display

  • On asymptotic behavior in time of solutions to nonlinear dispersive wave equations including Nonlinear Schrodinger, Klein-Gordon, Benjamin-Ono or Korteweg-de Vries equations
    Basic analysis-related


Academic Papers 【 display / non-display

  • Asymptotics in large time of solutions to nonlinear Schredinger and Hartree equations, N.Hayashi and P.I.Naumkin, Amer. J. Math., 1998.06, Papers

  • Higher-order nonlinear Schredinger equations with singular data, N. Hayashi, P. I. Naumkin, T. Ogawa, J. Evol. Equ.,18, 1, 263-276, 2018.03, Papers

  • Upper and lower time decay bounds for solutions of dissipative nonlinear Schredinger equations, N.Hayashi, C. Li, P.I. Naumkin, Commun. Pure Appl. Anal.,16, 6, 2089-2104, 2017.11, Papers

  • Damped wave equation with a critical nonlinearity in higher space dimensions, N.Hayashi, P.I. Naumkin, J. Math. Anal. Aanl.,446, (2017), 801-822, 2017.01, Papers

  • Scattering operator for the one dimensional Dirac equation with power nonlinearity, N.Hayashi, H.Sasaki, J. Hyperbolic Differential Equations,13, (2016) no. 4 (December), 821-832., 2016.12, Papers

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Books 【 display / non-display

  • Special, Asymptotics for Dissipative Nonlinear Equations, Elena.I.Kaikina, Pavel I. Naumkin and Ilja A. Shishmarev, Springer, 2006.04

  • Special, Nonlinear Theory of Pseudodifferential Equations with a Half Line, Nakao Hayashi, Elena.I.Kaikina, North-Holland Mathematics Studies, 2004.03

  • Special, Analytic Extension Formula and Their Applications, Saburou Saitoh, Nakao Hayashi and Masahiro Yamamoto, Kluwer Academic Publishers, 2001.09

Awards 【 display / non-display

  • Analysis award, Nakao Hayashi, 2008.09