Abstract
In this paper, we consider an initial-value problem for the Korteweg–de Vries equation. The normalized Korteweg–de Vries equation considered is given by where and represent dimensionless distance and time, respectively. In particular, we consider the case when the initial data has a discontinuous compressive step, where for and for . The method of matched asymptotic coordinate expansions is used to obtain the detailed large- asymptotic structure of the solution to this problem, which exhibits the formation of a dispersive shock wave.
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