Confluent Form of the Multistep ɛ-Algorithm, and the Relevant Integrable System

2011 ◽  
Vol 127 (2) ◽  
pp. 191-209 ◽  
Author(s):  
Claude Brezinski ◽  
Yi He ◽  
Xing-Biao Hu ◽  
Jian-Qing Sun ◽  
Hon-Wah Tam
Keyword(s):  
Integrable System ◽  
Confluent Form

On the Heisenberg Supermagnet Model in (2+1)-Dimensions

2017 ◽  
Vol 72 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Zhao-Wen Yan
Keyword(s):  
Integrable System ◽  
Integrable Systems ◽  
Bäcklund Transformations ◽  
Quadratic Constraints ◽  
Backlund Transformations

AbstractThe Heisenberg supermagnet model is an important supersymmetric integrable system in (1+1)-dimensions. We construct two types of the (2+1)-dimensional integrable Heisenberg supermagnet models with the quadratic constraints and investigate the integrability of the systems. In terms of the gage transformation, we derive their gage equivalent counterparts. Furthermore, we also construct new solutions of the supersymmetric integrable systems by means of the Bäcklund transformations.

scholarly journals Circular quiver gauge theories, isomonodromic deformations and $$W_N$$ fermions on the torus

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Fabrizio Del Monte ◽  
Pavlo Gavrylenko ◽  
Alessandro Tanzini
Keyword(s):  
Integrable System ◽  
Gauge Theories ◽  
The Self ◽  
Free Fermion ◽  
Two Dimensional ◽  
Isomonodromic Deformation ◽  
Specific Time ◽  
Dimensional Torus ◽  
Isomonodromic Deformations ◽  
Deformation Problem

AbstractWe study the relation between class $$\mathcal {S}$$ S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two-dimensional torus with punctures. Turning on the self-dual $$\Omega $$ Ω -background corresponds to a deautonomization of the Seiberg–Witten integrable system which implies a specific time dependence in its Hamiltonians. We show that the corresponding $$\tau $$ τ -function is proportional to the dual gauge theory partition function, the proportionality factor being a nontrivial function of the solution of the deautonomized Seiberg–Witten integrable system. This is obtained by mapping the isomonodromic deformation problem to $$W_N$$ W N free fermion correlators on the torus.

Limit Cycle Bifurcations of a Planar Near-Integrable System with Two Small Parameters

2021 ◽  
Vol 41 (4) ◽  
pp. 1034-1056
Author(s):  
Feng Liang ◽  
Maoan Han ◽  
Chaoyuan Jiang
Keyword(s):  
Limit Cycle ◽  
Integrable System ◽  
Small Parameters

scholarly journals Solution of tetrahedron equation and cluster algebras

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
P. Gavrylenko ◽  
M. Semenyakin ◽  
Y. Zenkevich
Keyword(s):  
Integrable System ◽  
Cluster Algebra ◽  
Newton Polygon ◽  
Cluster Algebras ◽  
Weyl Groups ◽  
Newton Polygons ◽  
Tetrahedron Equation ◽  
Affine Weyl Groups ◽  
New Formalism ◽  
Bruhat Cell

Abstract We notice a remarkable connection between the Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transformation is then identified with a sequence of four mutations. As an application of the new formalism, we show how to construct an integrable system with the spectral curve with arbitrary symmetric Newton polygon. Finally, we embed this integrable system into the double Bruhat cell of a Poisson-Lie group, show how triangular decomposition can be used to extend our approach to the general non-symmetric Newton polygons, and prove the Lemma which classifies conjugacy classes in double affine Weyl groups of A-type by decorated Newton polygons.

scholarly journals SCALING INVARIANCE IN A TIME-DEPENDENT ELLIPTICAL BILLIARD

2012 ◽  
Vol 22 (09) ◽  
pp. 1250207 ◽  
Author(s):  
DIEGO F. M. OLIVEIRA ◽  
MARKO ROBNIK
Keyword(s):  
Integrable System ◽  
Average Velocity ◽  
Moving Boundary ◽  
Time Dependent ◽  
Scaling Invariance ◽  
Energy Growth ◽  
Dynamical Properties ◽  
Scaling Arguments

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although the static elliptical billiard is an integrable system, after introducing time-dependent perturbation on the boundary the unlimited energy growth is observed. The behavior of the average velocity is described using scaling arguments.

A new integrable system: The interacting soliton of the BO

1995 ◽  
Vol 204 (5-6) ◽  
pp. 336-342 ◽  
Author(s):  
Benno Fuchssteiner ◽  
Thorsten Schulze
Keyword(s):  
Integrable System

Associative Cones and Integrable System

2006 ◽  
Vol 27 (2) ◽  
pp. 153-168 ◽  
Author(s):  
Chuu-Lian Terng* ◽  
Shengli Kong ◽  
Erxiao Wang
Keyword(s):  
Integrable System

scholarly journals Separation of Variables for a Lattice Integrable System and the Inverse Problem

2006 ◽  
Vol 45 (4) ◽  
pp. 820-834 ◽  
Author(s):  
Supriya Mukherjee ◽  
A. Ghose Choudhury ◽  
A. Roy Chowdhury
Keyword(s):  
Inverse Problem ◽  
Integrable System ◽  
Separation Of Variables

scholarly journals A new hierarchy of integrable system of1+2dimensions: from Newton's law to generalized Hamiltonian system. Part II

2006 ◽  
Vol 2006 ◽  
pp. 1-10
Author(s):  
Xuncheng Huang ◽  
Guizhang Tu
Keyword(s):  
Integrable System ◽  
Integrable Systems ◽  
Hamiltonian Equation ◽  
Hamiltonian Form ◽  
Fundamental Interest ◽  
Newton's Law ◽  
Newton’S Law ◽  
System Part ◽  
Generalized Hamiltonian System ◽  
Physical Laws

The Hamiltonian equation provides us an alternate description of the basic physical laws of motion, which is used to be described by Newton's law. The research on Hamiltonian integrable systems is one of the most important topics in the theory of solitons. This article proposes a new hierarchy of integrable systems of1+2dimensions with its Hamiltonian form by following the residue approach of Fokas and Tu. The new hierarchy of integrable system is of fundamental interest in studying the Hamiltonian systems.

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