DISPERSIVE RAREFACTION WAVE WITH A LARGE INITIAL GRADIENT

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 as...

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Bibliographic Details
Main Authors: Alexander E. Elbert, Sergey V. Zakharov
Format: Article
Language:English
Published: Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics 2017-07-01
Series:Ural Mathematical Journal
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Online Access:https://umjuran.ru/index.php/umj/article/view/68
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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.
ISSN:2414-3952