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ТМФ, 2002, том 133, номер 2, страницы 170–183 (Mi tmf388)  

Эта публикация цитируется в 402 научных статьях (всего в 402 статьях)

Новое интегрируемое уравнение с пиконными решениями

А. Дегасперисa, Д. Д. Холмb, А. Хонc

a University of Rome "La Sapienza"
b Los Alamos National Laboratory
c University of Kent

Аннотация: Рассмотрено новое дифференциальное уравнение в частных производных, имеющее вид, аналогичный виду уравнения мелкой воды Камасса–Холма, которое было недавно получено Дегасперисом и Прочези с использованием метода асимптотической интегрируемости. Доказывается точная интегрируемость нового уравнения путем построения его пары Лакса и объясняется связь этого уравнения с отрицательным потоком в иерархии Каупа–Купершмидта через преобразование взаимности. Бесконечная последовательность сохраняющихся величин выводится вместе с предложенной бигамильтоновой структурой. Уравнение допускает точные решения в виде суперпозиции мультипиконов. Описывается интегрируемая конечномерная динамика пиконов и сравнивается с аналогичными результатами для пиконов Камасса–Холма.

Ключевые слова: пиконы, преобразования взаимности, слабые решения

DOI: https://doi.org/10.4213/tmf388

Полный текст: PDF файл (293 kB)
Список литературы: PDF файл   HTML файл

Англоязычная версия:
Theoretical and Mathematical Physics, 2002, 133:2, 1463–1474

Реферативные базы данных:


Образец цитирования: А. Дегасперис, Д. Д. Холм, А. Хон, “Новое интегрируемое уравнение с пиконными решениями”, ТМФ, 133:2 (2002), 170–183; Theoret. and Math. Phys., 133:2 (2002), 1463–1474

Цитирование в формате AMSBIB
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\paper Новое интегрируемое уравнение с пиконными решениями
\jour ТМФ
\yr 2002
\vol 133
\issue 2
\pages 170--183
\mathnet{http://mi.mathnet.ru/tmf388}
\crossref{https://doi.org/10.4213/tmf388}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2001531}
\transl
\jour Theoret. and Math. Phys.
\yr 2002
\vol 133
\issue 2
\pages 1463--1474
\crossref{https://doi.org/10.1023/A:1021186408422}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000180061400004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Эта публикация цитируется в следующих статьяx:
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    32. Estevez, PG, “Singular manifold method for an equation in 2+1 dimensions”, Journal of Nonlinear Mathematical Physics, 12 (2005), 266  crossref  mathscinet  adsnasa  isi  scopus  scopus
    33. Lenells, J, “Traveling wave solutions of the Degasperis–Procesi equation”, Journal of Mathematical Analysis and Applications, 306:1 (2005), 72  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    34. В. Э. Адлер, А. Б. Шабат, “Одевающая цепочка для акустической спектральной задачи”, ТМФ, 149:1 (2006), 32–46  mathnet  crossref  mathscinet  zmath  adsnasa  elib; V. E. Adler, A. B. Shabat, “Dressing chain for the acoustic spectral problem”, Theoret. and Math. Phys., 149:1 (2006), 1324–1337  crossref  isi
    35. Ivanov, RI, “Extended Camassa-Holm hierarchy and conserved quantities”, Zeitschrift fur Naturforschung Section A-A Journal of Physical Sciences, 61:3–4 (2006), 133  zmath  isi
    36. Shen, JW, “Smooth and non-smooth travelling wave solutions of generalized Degasperis–Procesi equation”, Applied Mathematics and Computation, 182:2 (2006), 1418  crossref  mathscinet  zmath  isi  scopus  scopus
    37. Matsuno, Y, “Cusp and loop soliton solutions of short-wave models for the Camassa-Holm and Degasperis–Procesi equations”, Physics Letters A, 359:5 (2006), 451  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    38. Escher, J, “Global weak solutions and blow-up structure for the Degasperis–Procesi equation”, Journal of Functional Analysis, 241:2 (2006), 457  crossref  mathscinet  zmath  isi  scopus  scopus
    39. Liu, Y, “Global existence and blow-up phenomena for the Degasperis–Procesi equation”, Communications in Mathematical Physics, 267:3 (2006), 801  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    40. Liu, YQ, “Local well-posedness of a new integrable equation”, Nonlinear Analysis-Theory Methods & Applications, 64:11 (2006), 2516  crossref  mathscinet  zmath  isi  scopus  scopus
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    47. Zhang, GP, “Cuspons and smooth solitons of the Degasperis–Procesi equation under inhomogeneous boundary condition”, Mathematical Physics Analysis and Geometry, 10:3 (2007), 205  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    48. Tian, L, “Optimal control of the viscous Degasperis–Procesi equation”, Journal of Mathematical Physics, 48:11 (2007), 113513  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    49. Liu, Y, “On the Blow-up Phenomena for the Degasperis–Procesi Equation”, International Mathematics Research Notices, 2007, rnm117  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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