Yohei Tutiya

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It is well known that Sato theory was established by M.Sato around 1980 to give a unified viewpoint for integrable soliton equations [1]. A lot of important studies have been based on this magnificent theory since then. In this paper, we focus on one of the basic ideas of the theory, summarized as follows [2]. “Start from an ordinary differential equation(More)
In this paper, we present exact shock solutions of a coupled system of delay differential equations, which was introduced as a traffic-flow model called the car-following model. We use the Hirota method, originally developed in order to solve soliton equations. The relevant delay differential equations have been known to allow exact solutions expressed by(More)
We study an integro-differential equation which generalizes the periodic intermediate long wave (ILW) equation. The kernel of the singular integral involved is an elliptic function written as a second order difference of the Weierstrass ζ-function. Using Sato’s formulation, we show the integrability and construct some special solutions. An elliptic solution(More)
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