scholarly journals Differential equations for the radial limits in Z+2 of the solutions of a discrete integrable system

2018 ◽  
pp. 1-20
Author(s):  
Alexander Ivanovich Aptekarev ◽  
Rostyslav Kozhan
Keyword(s):  
Differential Equations ◽  
Integrable System ◽  
Discrete Integrable System ◽  
Radial Limits

CANONICAL BÄCKLUND TRANSFORMATION — A NEW DISCRETE INTEGRABLE SYSTEM AND BETHE ANSATZ

2005 ◽  
Vol 20 (18) ◽  
pp. 4355-4361
Author(s):  
SUPRIYA MUKHERJEE ◽  
A. ROY CHOWDHURY ◽  
A. GHOSE CHOUDHURY
Keyword(s):  
Explicit Form ◽  
Integrable System ◽  
Canonical Variable ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
R Matrix ◽  
Discrete Integrable System ◽  
Lax Operator ◽  
Bethe Equations ◽  
Quantization Problem

A new discrete Lax operator involving discrete canonical variable is introduced which generate new integrable system, and is analyzed in the light of the new concept of canonical Bäcklund transformation and classical r-matrix. The generating function of the transformation is explicitly deduced. The second half of the paper deals with the quantization problem where an explicit form of the Bethe equations are deduced.

Soliton Connection of the sinh-Gordon Equation

1984 ◽  
Vol 39 (9) ◽  
pp. 917-918 ◽  
Author(s):  
A. Grauel
Keyword(s):  
Differential Equations ◽  
Lie Algebra ◽  
Integrable System ◽  
Gordon Equation ◽  
Nonlinear Differential Equations ◽  
Differential Forms ◽  
Completely Integrable ◽  
Completely Integrable System ◽  
Derivatives Of

It is demonstrated that the sinh-Gordon equation can be written as covariant exterior derivatives of Lie algebra valued differential forms and, moreover, that these nonlinear differential equations represent a completely integrable system.

scholarly journals A New Discrete Integrable System Derived from a Generalized Ablowitz-Ladik Hierarchy and Its Darboux Transformation

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Xianbin Wu ◽  
Weiguo Rui ◽  
Xiaochun Hong
Keyword(s):  
Exact Solutions ◽  
Integrable System ◽  
Darboux Transformation ◽  
Dynamic Characteristics ◽  
Discrete System ◽  
Soliton Solutions ◽  
Interesting Phenomenon ◽  
Discrete Integrable System ◽  
New System

We find an interesting phenomenon that the discrete system appearing in a reference can be reduced to the old integrable system given by Merola, Ragnisco, and Tu in another reference. Differing from the works appearing in the above two references, a new discrete integrable system is obtained by the generalized Ablowitz-Ladik hierarchy; the Darboux transformation of this new discrete integrable system is established further. As applications of this Darboux transformation, different kinds of exact solutions of this new system are explicitly given. Investigatingthe properties of these exact solutions, we find that these exact solutions are not pure soliton solutions, but their dynamic characteristics are very interesting.

A HIERARCHY OF DISCRETE INTEGRABLE SYSTEM AND ITS COUPLED ENLARGED INTEGRABLE SYSTEM

2007 ◽  
Vol 21 (02n03) ◽  
pp. 155-161
Author(s):  
HAI-YONG DING ◽  
XIANG TIAN ◽  
XI-XIANG XU ◽  
HONG-XIANG YANG
Keyword(s):  
Spectral Problem ◽  
Integrable System ◽  
Soliton Equations ◽  
Discrete Integrable System ◽  
Zero Curvature Representation ◽  
Zero Curvature ◽  
Integrable Lattice ◽  
Integrable Couplings

A hierarchy of nonlinear integrable lattice soliton equations is derived from a discrete spectral problem. The hierarchy is proved to have discrete zero curvature representation. Using an enlarging algebra system [Formula: see text], we construct integrable couplings of the resulting hierarchy.

scholarly journals The Pentagram Map: A Discrete Integrable System

2010 ◽  
Vol 299 (2) ◽  
pp. 409-446 ◽  
Author(s):  
Valentin Ovsienko ◽  
Richard Schwartz ◽  
Serge Tabachnikov
Keyword(s):  
Integrable System ◽  
Discrete Integrable System ◽  
Pentagram Map
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