an:07255624
Zbl 1448.35442
Elbert, Alexander E.; Zakharov, Sergey V.
Dispersive rarefaction wave with a large initial gradient
EN
Ural Math. J. 3, No. 1, 33-43 (2017).
00453651
2017
j
35Q53 35B40 35C20 35B25 65D32
Korteweg-de Vries; Cauchy problem; asymptotic behavior; rarefaction wave
Summary: Consider the Cauchy problem for the Korteweg-de Vries equation with a small parameter at the highest derivative and a large gradient of the initial function. Numerical and analytical methods show that the obtained using renormalization formal asymptotics, corresponding to rarefaction waves, is an asymptotic solution of the KdV equation. The graphs of the asymptotic solutions are represented, including the case of non-monotonic initial data.