scholarly journals Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations

2017 ◽  
Vol 473 (2203) ◽  
pp. 20160915 ◽  
Author(s):  
Wei Fu ◽  
Frank W. Nijhoff
Keyword(s):  
Integrable Systems ◽  
General Class ◽  
Solution Structure ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Unified Framework ◽  
Discrete Integrable Systems

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

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.

scholarly journals On non-autonomous differential-difference AKP, BKP and CKP equations

2021 ◽  
Vol 477 (2245) ◽  
pp. 20200717
Author(s):  
Wei Fu ◽  
Frank W. Nijhoff
Keyword(s):  
Integral Equation ◽  
Difference Equations ◽  
Integrable Systems ◽  
Three Dimensional ◽  
Linear Integral Equation ◽  
Discrete Integrable Systems ◽  
Link Type ◽  
Direct Linearization ◽  
The One ◽  
Linear Integral

Based on the direct linearization framework of the discrete Kadomtsev–Petviashvili-type equations presented in the work of Fu & Nijhoff (Fu W, Nijhoff FW. 2017 Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations. Proc. R. Soc. A 473 , 20160915 ( doi:10.1098/rspa.2016.0915 )), six novel non-autonomous differential-difference equations are established, including three in the AKP class, two in the BKP class and one in the CKP class. In particular, one in the BKP class and the one in the CKP class are both in (2 + 2)-dimensional form. All the six models are integrable in the sense of having the same linear integral equation representations as those of their associated discrete Kadomtsev–Petviashvili-type equations, which guarantees the existence of soliton-type solutions and the multi-dimensional consistency of these new equations from the viewpoint of the direct linearization.

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-Dimensional Solution Structure ofSaccharomyces cerevisiaeReduced Iso-1-cytochromec†

Biochemistry ◽  
1996 ◽  
Vol 35 (43) ◽  
pp. 13788-13796 ◽  
Author(s):  
Paolo Baistrocchi ◽  
Lucia Banci ◽  
Ivano Bertini ◽  
Paola Turano ◽  
Kara L. Bren ◽  
...  
Keyword(s):  
Solution Structure ◽  
Three Dimensional ◽  
Dimensional Solution
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