an:07278474
Zbl 07278474
Zakharov, Serge?? Viktorovich; ??l'bert, Aleksandr Evgen'evich
Modelling compression waves with a large initial gradient in the Korteweg-de Vries hydrodynamics
RU
Ufim. Mat. Zh. 9, No. 1, 42-54 (2017); translation in Ufa Math. J. 9, No. 1, 41-53 (2017).
00455627
2017
j
35Q53
Korteweg-de Vries equation; Cauchy problem; compression wave
Summary: We consider the Cauchy problem for the Korteweg-de Vries equation 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 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.