scholarly journals On an integrable deformation of the Kowalevski top

2014 ◽  
pp. 223-236 ◽  
Author(s):  
A. V. Vershilov ◽  
◽  
Y. A. Grigoryev ◽  
A. V. Tsiganov ◽  
◽  
...  
Keyword(s):  
Integrable Deformation ◽  
Kowalevski Top

Embeddings for the space on sets of finite perimeter

2019 ◽  
Vol 150 (5) ◽  
pp. 2442-2461 ◽  
Author(s):  
Nikolai V. Chemetov ◽  
Anna L. Mazzucato
Keyword(s):  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Rigid Bodies ◽  
Deformation Tensor ◽  
Integrable Deformation ◽  
Sets Of Finite Perimeter ◽  
Open Set ◽  
Finite Perimeter ◽  
Continuous Embedding

AbstractGiven an open set with finite perimeter $\Omega \subset {\open R}^n$, we consider the space $LD_\gamma ^{p}(\Omega )$, $1\les p<\infty $, of functions with pth-integrable deformation tensor on Ω and with pth-integrable trace value on the essential boundary of Ω. We establish the continuous embedding $LD_\gamma ^{p}(\Omega )\subset L^{pN/(N-1)}(\Omega )$. The space $LD_\gamma ^{p}(\Omega )$ and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid.

scholarly journals On the integrable deformations of a system related to the motion of two vortices in an ideal incompressible fluid

2019 ◽  
Vol 29 ◽  
pp. 01015 ◽  
Author(s):  
Cristian Lăzureanu ◽  
Ciprian Hedrea ◽  
Camelia Petrişor
Keyword(s):  
Incompressible Fluid ◽  
Mechanical System ◽  
Integrable Systems ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Ideal Incompressible Fluid ◽  
First Integrals ◽  
Integrable Deformation ◽  
Integrable Deformations ◽  
The Given

Altering the first integrals of an integrable system integrable deformations of the given system are obtained. These integrable deformations are also integrable systems, and they generalize the initial system. In this paper we give a method to construct integrable deformations of maximally superintegrable Hamiltonian mechanical systems with two degrees of freedom. An integrable deformation of a maximally superintegrable Hamiltonian mechanical system preserves the number of first integrals, but is not a Hamiltonian mechanical system, generally. We construct integrable deformations of the maximally superintegrable Hamiltonian mechanical system that describes the motion of two vortices in an ideal incompressible fluid, and we show that some of these integrable deformations are Hamiltonian mechanical systems too.

INTEGRABLE DEFORMATIONS OF THE NONUNITARY MINIMAL CONFORMAL MODEL ℳ3,5

1992 ◽  
Vol 07 (20) ◽  
pp. 5027-5044 ◽  
Author(s):  
G. MUSSARDO
Keyword(s):  
Field Theories ◽  
Conformal Space ◽  
One Dimensional ◽  
Conformal Model ◽  
Integrable Deformation ◽  
Anomalous Dimensions ◽  
Integrable Deformations ◽  
Scaling Region ◽  
The One ◽  
Space Approach

The scaling region of the nonunitary minimal conformal model M3,5 is described by three different integrable massive field theories. We propose the scattering theory for the integrable deformation of M3,5 by the field ψ with anomalous dimensions [Formula: see text]. The spectrum of this theory is confirmed by the Truncation Conformal Space Approach. We also consider the thermodynamics of the one-dimensional quantum system defined by the transfer matrix relative to the deformation of M3,5 by the field φ with anomalous dimensions [Formula: see text]. This deformation drives the original conformal model into a region of the phase diagram where there are plasma oscillations.

scholarly journals Multicomponent Nonlinear Evolution Equations of the Heisenberg Ferromagnet Type: Local Versus Nonlocal Reductions

2021 ◽  
pp. 274-285
Author(s):  
Tihomir Valchev
Keyword(s):  
Heisenberg Model ◽  
Symmetric Spaces ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Heisenberg Ferromagnet ◽  
Lax Pairs ◽  
Hermitian Symmetric Spaces ◽  
Integrable Deformation

This work is dedicated to systems of matrix nonlinear evolution equations related to Hermitian symmetric spaces of the type $\mathbf{A.III}$. The systems under consideration generalize the $1+1$ dimensional Heisenberg ferromagnet equation in the sense that their Lax pairs are linear bundles in pole gauge like for the original Heisenberg model. Here we present certain local and nonlocal reductions. A local integrable deformation and some of its reductions are discussed as well.

scholarly journals Three-parameter integrable deformation of ℤ4 permutation supercosets

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
F. Delduc ◽  
B. Hoare ◽  
T. Kameyama ◽  
S. Lacroix ◽  
M. Magro
Keyword(s):  
Integrable Deformation

Integrable deformation of critical surfaces in spaceforms

2013 ◽  
Vol 44 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Michael Deutsch
Keyword(s):  
Integrable Deformation

scholarly journals Poisson maps and integrable deformations of the Kowalevski top

2003 ◽  
Vol 36 (29) ◽  
pp. 8035-8048 ◽  
Author(s):  
I V Komarov ◽  
V V Sokolov ◽  
A V Tsiganov
Keyword(s):  
Integrable Deformations ◽  
Kowalevski Top
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