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We consider the long-time evolution of pulses in the Korteweg-de Vriesequation theory for initial distributions which produce no soliton, but insteadlead to the formation of a dispersive shock wave and of a rarefaction wave. Anapproach based on Whitham modulation theory makes it possible to obtain ananalytic description of the structure and to describe its self-similar behaviornear the soliton edge of the shock. The results are compared with numericalsimulations.

Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons revisited: Whitham method