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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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
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/68 |
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| _version_ | 1849397171603898368 |
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| author | Alexander E. Elbert Sergey V. Zakharov |
| author_facet | Alexander E. Elbert Sergey V. Zakharov |
| author_sort | Alexander E. Elbert |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ef2e00843a594f2ebcd2a2317d38b718 |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2017-07-01 |
| publisher | 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 |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-ef2e00843a594f2ebcd2a2317d38b7182025-08-20T03:39:06ZengUral 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 MechanicsUral Mathematical Journal2414-39522017-07-013110.15826/umj.2017.1.00230DISPERSIVE RAREFACTION WAVE WITH A LARGE INITIAL GRADIENTAlexander E. Elbert0Sergey V. Zakharov1N.N.Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, EkaterinburgN.N.Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, EkaterinburgConsider 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.https://umjuran.ru/index.php/umj/article/view/68The Korteweg--de VriesCauchy problemAsymptotic behaviorRarefaction wave |
| spellingShingle | Alexander E. Elbert Sergey V. Zakharov DISPERSIVE RAREFACTION WAVE WITH A LARGE INITIAL GRADIENT Ural Mathematical Journal The Korteweg--de Vries Cauchy problem Asymptotic behavior Rarefaction wave |
| title | DISPERSIVE RAREFACTION WAVE WITH A LARGE INITIAL GRADIENT |
| title_full | DISPERSIVE RAREFACTION WAVE WITH A LARGE INITIAL GRADIENT |
| title_fullStr | DISPERSIVE RAREFACTION WAVE WITH A LARGE INITIAL GRADIENT |
| title_full_unstemmed | DISPERSIVE RAREFACTION WAVE WITH A LARGE INITIAL GRADIENT |
| title_short | DISPERSIVE RAREFACTION WAVE WITH A LARGE INITIAL GRADIENT |
| title_sort | dispersive rarefaction wave with a large initial gradient |
| topic | The Korteweg--de Vries Cauchy problem Asymptotic behavior Rarefaction wave |
| url | https://umjuran.ru/index.php/umj/article/view/68 |
| work_keys_str_mv | AT alexandereelbert dispersiverarefactionwavewithalargeinitialgradient AT sergeyvzakharov dispersiverarefactionwavewithalargeinitialgradient |