Five-Dimensional Lax-Integrable Equation, Its Reductions and Recursion Operator

被引：9

作者：

Baran, H. ^{[1
]}

Krasil'shchik, I. S. ^{[1
,2
]}

Morozov, O. I. ^{[3
]}

Vojcak, P. ^{[1
]}

机构：

[1] Silesian Univ Opava, Math Inst, Rybnicku 1, Opava 74601, Czech Republic

[2] Independent Univ Moscow, B Vlasevsky 11, Moscow 119002, Russia

[3] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2015年 / 36卷 / 03期

关键词：

integrable systems; recursion operators; symmetries; conservation laws; differential coverings;

D O I：

10.1134/S1995080215030026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a five-dimensional nonlinear PDE associated to the five-dimensional equation introduced by Martinez Alonso and Shabat. For our equation we find differential coverings with non-removable parameters and list its reductions to known 4D and 3D integrable equations. One of the coverings produces a new family of integrable 5D equations. We show that each pair of these equations is related by a Backlund transformation, including the Backlund auto-transformation for each equation from the family. Also we find a recursion operator for symmetries of the equation and study its action.

引用

页码：225 / 233

页数：9

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