Analytic Representation of Traveling Wave Solution and Dispersive Relation in Tyson's Model

The researches on traveling wave solution and dispersive relation in Tyson's model were only confined to numerical simulation and theoretically formal expression in the past, because of lack of the analytic representation of speed of the traveling wave. In this paper we give its analytic expression by Painlevé analysis, and so we can obtain the explicit representation of traveling wave solution and dispersive relation.