scholarly journals Discrete integrable systems: Multidimensional consistency

2020 ◽  
Vol 69 (1) ◽  
pp. 010202
Author(s):  
Da-Jun Zhang
Keyword(s):  
Integrable Systems ◽  
Discrete Integrable Systems ◽  
Multidimensional Consistency

scholarly journals Manin Involutions for Elliptic Pencils and Discrete Integrable Systems

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Matteo Petrera ◽  
Yuri B. Suris ◽  
Kangning Wei ◽  
René Zander
Keyword(s):  
Integrable Systems ◽  
Geometric Description ◽  
Discrete Integrable Systems ◽  
Birational Maps ◽  
Base Points ◽  
Special Geometry ◽  
Low Degree ◽  
Geometric Study

AbstractWe contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.

scholarly journals Discrete integrable systems generated by Hermite-Padé approximants

Nonlinearity ◽  
2016 ◽  
Vol 29 (5) ◽  
pp. 1487-1506 ◽  
Author(s):  
Alexander I Aptekarev ◽  
Maxim Derevyagin ◽  
Walter Van Assche
Keyword(s):  
Integrable Systems ◽  
Padé Approximants ◽  
Discrete Integrable Systems ◽  
Pade Approximants

Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions

Nonlinearity ◽  
2015 ◽  
Vol 28 (7) ◽  
pp. 2279-2306 ◽  
Author(s):  
Xiao-Min Chen ◽  
Xiang-Ke Chang ◽  
Jian-Qing Sun ◽  
Xing-Biao Hu ◽  
Yeong-Nan Yeh
Keyword(s):  
Orthogonal Polynomials ◽  
Integrable Systems ◽  
Discrete Integrable Systems

scholarly journals Direct linearization approach to discrete integrable systems associated with ℤ 𝒩 graded Lax pairs

2020 ◽  
Vol 476 (2237) ◽  
pp. 20200036
Author(s):  
Wei Fu
Keyword(s):  
Difference Equations ◽  
Bilinear Form ◽  
Integrable Systems ◽  
Solution Structure ◽  
Discrete Systems ◽  
Lax Pairs ◽  
Discrete Integrable Systems ◽  
Direct Linearization ◽  
Linear Integral ◽  
Linear Integral Equations

Fordy and Xenitidis [ J. Phys. A: Math. Theor. 50 (2017) 165205. ( doi:10.1088/1751-8121/aa639a )] recently proposed a large class of discrete integrable systems which include a number of novel integrable difference equations, from the perspective of Z N graded Lax pairs, without providing solutions. In this paper, we establish the link between the Fordy–Xenitidis (FX) discrete systems in coprime case and linear integral equations in certain form, which reveals solution structure of these equations. The bilinear form of the FX integrable difference equations is also presented together with the associated general tau function. Furthermore, the solution structure explains the connections between the FX novel models and the discrete Gel’fand–Dikii hierarchy.

Sign in / Sign up

Export Citation Format

Share Document