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

共 50 条

[1] Bargmann-Type Finite-Dimensional Reductions of the Lax-Integrable Supersymmetric Boussinesq Hierarchy and Their Integrability
Hentosh O.E.
[J]. Journal of Mathematical Sciences, 2017, 220 (4) : 402 - 424
[2] A LAX-INTEGRABLE EQUATION SUGGESTIVE OF A HIERARCHY OF SOLITON-EQUATIONS
WILLOX, R
LAMBERT, F
[J]. INVERSE PROBLEMS, 1991, 7 (06) : L45 - L48
[3] A five-dimensional form of the Dirac equation
Kocinski, J
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1999, 32 (23): : 4257 - 4277
[4] Five-dimensional gauge theories and relativistic integrable systems
Nekrasov, N
[J]. NUCLEAR PHYSICS B, 1998, 531 (1-3) : 323 - 344
[5] Higher-dimensional integrable models with a common recursion operator
Lou, SY
[J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 1997, 28 (01) : 41 - 50
[6] Time-like reductions of five-dimensional supergravity
V. Cortés
P. Dempster
T. Mohaupt
[J]. Journal of High Energy Physics, 2014
[7] Time-like reductions of five-dimensional supergravity
Cortes, V.
Dempster, P.
Mohaupt, T.
[J]. JOURNAL OF HIGH ENERGY PHYSICS, 2014, (04):
[8] Lax-integrable Laberge–Mathieu hierarchy of supersymmetric nonlinear dynamical systems and its finite-dimensional reduction of Neumann type
O. E. Hentosh
[J]. Ukrainian Mathematical Journal, 2009, 61 : 1075 - 1092
[9] LAX-INTEGRABLE LABERGE-MATHIEU HIERARCHY OF SUPERSYMMETRIC NONLINEAR DYNAMICAL SYSTEMS AND ITS FINITE-DIMENSIONAL REDUCTION OF NEUMANN TYPE
Hentosh, O. E.
[J]. UKRAINIAN MATHEMATICAL JOURNAL, 2009, 61 (07) : 1075 - 1092
[10] Higher symmetries of cotangent coverings for Lax-integrable multi-dimensional partial differential equations and Lagrangian deformations
Baran, H.
Krasil'shchik, I. S.
Morozov, O. I.
Vojcak, P.
[J]. PHYSICS AND MATHEMATICS OF NONLINEAR PHENOMENA 2013 (PMNP2013), 2014, 482

← 1 2 3 4 5 →