Integrable deformation of critical surfaces in spaceforms

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

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

Analytic deformations of pencils and integrable one-forms having a first integral

2020 ◽  
Vol 31 (11) ◽  
pp. 2050089
Author(s):  
Bruno Scárdua
Keyword(s):  
Singular Point ◽  
First Integral ◽  
Product Formula ◽  
Analytic Family ◽  
Analytic Subset ◽  
Integrable Deformation ◽  
Codimension One ◽  
Dimension Formula ◽  
Geometric Conditions ◽  
Simply Connected

We consider integrable analytic deformations of codimension one holomorphic foliations near an initially singular point. Such deformations are of two possible types. The first type is given by an analytic family [Formula: see text] of integrable one-forms [Formula: see text] defined in a neighborhood [Formula: see text] of the initial singular point, and parametrized by the disc [Formula: see text]. The initial foliation is defined by [Formula: see text]. The second type, more restrictive, is given by an integrable holomorphic one-form [Formula: see text] defined in the product [Formula: see text]. Then, the initial foliation is defined by the slice restriction [Formula: see text]. In the first part of this work, we study the case where the starting foliation has a holomorphic first integral, i.e. it is given by [Formula: see text] for some germ of holomorphic function [Formula: see text] at the origin [Formula: see text]. We assume that the germ [Formula: see text] is irreducible and that the typical fiber of [Formula: see text] is simply-connected. This is the case if outside of a dimension [Formula: see text] analytic subset [Formula: see text], the analytic hypersurface [Formula: see text] has only normal crossings singularities. We then prove that, if cod sing [Formula: see text] then the (germ of the) developing foliation given by [Formula: see text] also exhibits a holomorphic first integral. For the general case, i.e. cod sing [Formula: see text], we obtain a dimension two normal form for the developing foliation. In the second part of the paper, we consider analytic deformations [Formula: see text], of a local pencil [Formula: see text], for [Formula: see text]. For dimension [Formula: see text] we consider [Formula: see text]. For dimension [Formula: see text] we assume some generic geometric conditions on [Formula: see text] and [Formula: see text]. In both cases, we prove: (i) in the case of an analytic deformation there is a multiform formal first integral of type [Formula: see text] with some properties; (ii) in the case of an integrable deformation there is a meromorphic first integration of the form [Formula: see text] with some additional properties, provided that for [Formula: see text] the axes remain invariant for the foliations [Formula: see text].

SYMMETRY, INTEGRABILITY AND DEFORMATIONS OF LONG-RANGE INTERACTING HAMILTONIANS

1999 ◽  
Vol 13 (24n25) ◽  
pp. 2903-2908 ◽  
Author(s):  
ANGEL BALLESTEROS
Keyword(s):  
Long Range ◽  
Hamiltonian Systems ◽  
Quantum Algebra ◽  
Complete Integrability ◽  
Quantum Algebras ◽  
R Matrix ◽  
Completely Integrable ◽  
Integrable Deformation ◽  
Coalgebra Structure ◽  
Integrable Deformations

The notion of coalgebra symmetry in Hamiltonian systems is analysed. It is shown how the complete integrability of some long-range interacting Hamiltonians can be extracted from their associated coalgebra structure with no use of a quantum R-matrix. Within this framework, integrable deformations can be considered as direct consequences of the introduction of coalgebra deformations (quantum algebras). As an example, the Gaudin magnet is derived from a sl(2) coalgebra, and a completely integrable deformation of this Hamiltonian is obtained through a twisted gl(2) quantum algebra.

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