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In this paper, we present a new hierarchy which includes the intermediate long wave (ILW) equation at the lowest order. This hierarchy is thought to be a novel reduction of the 1st modified KP type hierarchy. The framework of our investigation is Sato theory.
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)