Article
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.
DOI:10.13108/2017-9-1-41
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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.