Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution
The modified Korteveg{de Vries equation on the line is considered. The initial function is a discontinuous and piece-wise constant step function, i.e. q(x, 0) = cr for x ≥ 0 and q(x, 0) = cl for x < 0, where cl, cr are real numbers which satisfy cl > cr > 0. The goal of this paper is to stu...
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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2012
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106707 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution / V. Kotlyarov, A. Minakov // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 1. — С. 38-62. — Бібліогр.: 49 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-106707 |
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irk-123456789-1067072016-10-04T03:02:16Z Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution Kotlyarov, V. Minakov, A. The modified Korteveg{de Vries equation on the line is considered. The initial function is a discontinuous and piece-wise constant step function, i.e. q(x, 0) = cr for x ≥ 0 and q(x, 0) = cl for x < 0, where cl, cr are real numbers which satisfy cl > cr > 0. The goal of this paper is to study the asymptotic behavior of the solution of the initial-value problem as t → ∞. Рассматривается модифицированное уравнение КдФ на всей прямой с начальным условием типа ступеньки, которая равна константе cl при x < 0 и другой константе cr при x > 0. При этом выполняется условие cl > cr > 0, что обеспечивает режим "гидродинамической волны сжатия" при t → ∞. Цель статьи - изучение асимптотического поведения решения начально-краевой задачи, когда t → ∞. 2012 Article Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution / V. Kotlyarov, A. Minakov // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 1. — С. 38-62. — Бібліогр.: 49 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106707 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The modified Korteveg{de Vries equation on the line is considered. The initial function is a discontinuous and piece-wise constant step function, i.e. q(x, 0) = cr for x ≥ 0 and q(x, 0) = cl for x < 0, where cl, cr are real numbers which satisfy cl > cr > 0. The goal of this paper is to study the asymptotic behavior of the solution of the initial-value problem as t → ∞. |
| format |
Article |
| author |
Kotlyarov, V. Minakov, A. |
| spellingShingle |
Kotlyarov, V. Minakov, A. Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution Журнал математической физики, анализа, геометрии |
| author_facet |
Kotlyarov, V. Minakov, A. |
| author_sort |
Kotlyarov, V. |
| title |
Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution |
| title_short |
Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution |
| title_full |
Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution |
| title_fullStr |
Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution |
| title_full_unstemmed |
Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution |
| title_sort |
step-initial function to the mkdv equation: hyper-elliptic long-time asymptotics of the solution |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106707 |
| citation_txt |
Step-Initial Function to the MKdV Equation: Hyper-Elliptic Long-Time Asymptotics of the Solution / V. Kotlyarov, A. Minakov // Журнал математической физики, анализа, геометрии. — 2012. — Т. 8, № 1. — С. 38-62. — Бібліогр.: 49 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
AT kotlyarovv stepinitialfunctiontothemkdvequationhyperellipticlongtimeasymptoticsofthesolution AT minakova stepinitialfunctiontothemkdvequationhyperellipticlongtimeasymptoticsofthesolution |
| first_indexed |
2023-10-18T20:13:31Z |
| last_indexed |
2023-10-18T20:13:31Z |
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1796149300872347648 |