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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)

- Y Tutiya, M Kanai
- 2007

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)

- Jun’ichi Shiraishiand, Yohei Tutiya
- 2009

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)

- Yohei Tutiya, Jun'ichi Shiraishi
- Mathematics and Computers in Simulation
- 2012

- Yohei TUTIYA
- 2006

The integral sign with a backslash denotes the principal value. The constant σ is taken to be ±1. For positive (negative) σ, the equation is called the defocusing (focusing) INLS equation. Originally, the defocusing INLS equation was discovered by carrying out a reductive perturbation method for the ILW equation [8]. It describes the long–term evolution of… (More)

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