Nonabelian [IMG align=ABSMIDDLE alt=$ \mathfrak{so}_3$]tex_rm_5256_img1[/IMG] Euler top

2021 ◽  
Vol 76 (1) ◽  
Author(s):  
Vladimir Vyacheslavovich Sokolov
Keyword(s):  
Euler Top

Nonholonomic deformation of coupled and supersymmetric KdV equations and Euler–Poincaré–Suslov method

2015 ◽  
Vol 27 (04) ◽  
pp. 1550011 ◽  
Author(s):  
Partha Guha
Keyword(s):  
Kdv Equation ◽  
Infinite Dimensional ◽  
Kdv Equations ◽  
Finite Dimensional ◽  
Euler Top ◽  
Two Component ◽  
Finite Dimensional Case ◽  
Coupled Kdv Equations ◽  
The Right ◽  
Supersymmetric Kdv Equation

Recently, Kupershmidt [38] presented a Lie algebraic derivation of a new sixth-order wave equation, which was proposed by Karasu-Kalkani et al. [31]. In this paper, we demonstrate that Kupershmidt's method can be interpreted as an infinite-dimensional analogue of the Euler–Poincaré–Suslov (EPS) formulation. In a finite-dimensional case, we modify Kupershmidt's deformation of the Euler top equation to obtain the standard EPS construction on SO(3). We extend Kupershmidt's infinite-dimensional construction to construct a nonholonomic deformation of a wide class of coupled KdV equations, where all these equations follow from the Euler–Poincaré–Suslov flows of the right invariant L2 metric on the semidirect product group [Formula: see text], where Diff (S1) is the group of orientation preserving diffeomorphisms on a circle. We generalize our construction to the two-component Camassa–Holm equation. We also give a derivation of a nonholonomic deformation of the N = 1 supersymmetric KdV equation, dubbed as sKdV6 equation and this method can be interpreted as an infinite-dimensional supersymmetric analogue of the Euler–Poincaré–Suslov (EPS) method.

A Lax pair of the discrete Euler top

2017 ◽  
Vol 50 (24) ◽  
pp. 245203 ◽  
Author(s):  
Kinji Kimura
Keyword(s):  
Lax Pair ◽  
Euler Top

Integrability of the discretization of the controlled Euler Top

2010 ◽  
Vol 215 (12) ◽  
pp. 4185-4190
Author(s):  
Supriya Mukherjee ◽  
Sourav Dutta
Keyword(s):  
Euler Top

GENERAL EULER TOP SYSTEM AND ITS LAX REPRESENTATION

2011 ◽  
Vol 08 (05) ◽  
pp. 937-944 ◽  
Author(s):  
GHEORGHE IVAN ◽  
MIHAI IVAN
Keyword(s):  
Lax Representation ◽  
Euler Top

The main purpose of this paper is to give the Lax representation of the general Euler top system.

scholarly journals Arithmetic Euler top

2017 ◽  
Vol 173 ◽  
pp. 37-63 ◽  
Author(s):  
Alexandru Buium ◽  
Emma Previato
Keyword(s):  
Euler Top

scholarly journals Higher-dimensional generalisations of the Euler top equations

1998 ◽  
Vol 240 (3) ◽  
pp. 132-136 ◽  
Author(s):  
David B Fairlie ◽  
Tatsuya Ueno
Keyword(s):  
Higher Dimensional ◽  
Euler Top

scholarly journals The Euler top and canonical lifts

2018 ◽  
Vol 190 ◽  
pp. 156-168
Author(s):  
Alexandru Buium ◽  
Emma Previato
Keyword(s):  
Euler Top

scholarly journals Remarks on N=1 supersymmetric extension of the Euler top

2022 ◽  
pp. 115668
Author(s):  
Anton Galajinsky
Keyword(s):  
Supersymmetric Extension ◽  
Euler Top

scholarly journals Bianchi-IX, Darboux–Halphen and Chazy–Ramanujan

2016 ◽  
Vol 13 (04) ◽  
pp. 1650042 ◽  
Author(s):  
Sumanto Chanda ◽  
Partha Guha ◽  
Raju Roychowdhury
Keyword(s):  
Vacuum Einstein Equation ◽  
Yang Mills ◽  
Gravitational Instanton ◽  
Self Duality ◽  
Bianchi Ix ◽  
Euler Top ◽  
Integrable Dynamical Systems ◽  
Halphen System ◽  
Special Case ◽  
Dual Case

Bianchi-IX four metrics are SU(2) invariant solutions of vacuum Einstein equation, for which the connection-wise self-dual case describes the Euler top, while the curvature-wise self-dual case yields the Ricci flat classical Darboux–Halphen system. It is possible to see such a solution exhibiting Ricci flow. The classical Darboux–Halphen system is a special case of the generalized one that arises from a reduction of the self-dual Yang–Mills equation and the solutions to the related homogeneous quadratic differential equations provide the desired metric. A few integrable and near-integrable dynamical systems related to the Darboux–Halphen system and occurring in the study of Bianchi-IX gravitational instanton have been listed as well. We explore in details whether self-duality implies integrability.

Spectral Asymptotic for the High-Dimensional Euler Top

2008 ◽  
Vol 86 (1) ◽  
pp. 47-52
Author(s):  
Alain Bourget
Keyword(s):  
High Dimensional ◽  
Euler Top
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