43836

Автор(ы): 

Автор(ов): 

4

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

2D reductions of the equation $u_{yy} = u_{tx} + u_y u_{xx} −u_x u_{xy}$ and their nonlocal symmetries

ISBN/ISSN: 

Print ISSN: 1402-9251 Online ISSN: 1776-0852

DOI: 

https://doi.org/10.1080/14029251.2017.1418052

Наименование источника: 

  • Journal of Nonlinear Mathematical Physics

Обозначение и номер тома: 

Vol. 24, Supplement 1

Город: 

  • Швеция

Издательство: 

  • Luleaa University of Technology

Год издания: 

2017

Страницы: 

36–47
Аннотация
We consider the 3D equation $u_{yy} =u_{tx} +u_y u_{xx} −u_x u_{xy}$ and its 2D symmetry reductions: (1) $u_{yy} = (u_y +y)u_{xx} − u_x u_{xy} −2$ (which is equivalent to the Gibbons-Tsarev equation) and (2) $u_{yy} = (u_y +2x)u_{xx} +(y−u_x)u_{xy} − u_x$. Using the corresponding reductions of the known Lax pair for the 3D equation, we describe nonlocal symmetries of (1) and (2) and show that the Lie algebras of these symmetries are isomorphic to the Witt algebra.

Библиографическая ссылка: 

Красильщик И.С., Morozov O.I., Vojcak P., Holba P. 2D reductions of the equation $u_{yy} = u_{tx} + u_y u_{xx} −u_x u_{xy}$ and their nonlocal symmetries // Journal of Nonlinear Mathematical Physics. 2017. Vol. 24, Supplement 1. С. 36–47.