Ryogo Hirota

Ryōgo Hirota ( Japanese 広 田 良 吾 , Hirota Ryōgo ; * 1932 ; † 2015 ) was a Japanese physicist and applied mathematician.

In the early 1970s he was at the RCA research laboratories in Tokyo and in the late 1970s at the engineering faculty at Hiroshima University .

A system of soliton equations for shallow water waves is named after Hirota and Junkichi Satsuma (1976).

Direct method developer

Hirota developed the direct method of solving soliton equations ( nonlinear evolution equations) in the early 1970s , which is simpler than the inverse scattering transformation method developed in the late 1960s.

The direct method was expanded in the 1980s in the school of Mikio Satō ( Michio Jimbō , Etsurō Date, Tetsuji Miwa and Masaki Kashiwara ) and associated with infinite-dimensional Lie algebras and their representations .

Action

The direct method is to transform the dependent variable so that the solution becomes a sum of exponential functions . The original solution sought is transformed to the tau function and new equations are considered bilinear in the tau function and its derivatives . ${\displaystyle u}$ ${\displaystyle u=2{\frac {d^{2}}{{dx}^{2}}}\log {(\tau })}$

application

The method played an essential role in solving the Schottky problem using the KP equation and was also applied to ordinary and partial difference equations .

Discrete equations are examined in connection with the direct method are provided by Miwa and the discrete analogue of the generalized Toda equations (DAGTE, discrete analogue of the generalized Toda equation ) of Hirota.

Fonts

• Exact Solution of the Korteweg — de Vries Equation for Multiple Collisions of Solitons. Phys. Rev. Lett., Vol. 27, 1971, p. 1192
• Direct methods in soliton theory. in: RK Bullough, PJ Caudrey: Solitons, Topics in Current Physics 17, Springer 1980
• The Direct Method in Soliton Theory. Cambridge University Press 2004 (first published in 1992 in Japan)

literature

• Biography with photo in: J. Hieratina, N. Joshi, FW Nijhoff: Discrete Systems and Integrability. Cambridge University Press 2016, p. 223.

Individual evidence

1. ↑ Hirota, Satsuma: N-Soliton Solutions of Model Equations for Shallow Water Waves, Journal of the Physical Society of Japan, Volume 40, 1976, p. 611