Ufa Mathematical Journal
    Volume 9, Number 1, pp. 41-53

    Modelling compression waves with a large initial gradient in the Korteweg--de Vries hydrodynamics

    Elbert A.E., Zakharov S.V.


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    We consider the Cauchy problem for the Korteweg-de Vries equations with a small parameter at the higher derivative and a large gradient of the initial function. By means of the numerical and analytic methods we show that the formal asymptotics obtained by a renormalization is an asymptotic solution to the KdV equation. We obtain the graphs of the asymptotic solutions including the case of non-monotone initial data.