6 citations · 22 across the 22 of their papers we have counts for
23 papers
Integrable discretizations for a generalized sine-Gordon equation and the reductions to the sine-Gordon equation and the short pulse equation
Han-Han Sheng, Bao-Feng Feng, Guo-Fu Yu
In this paper, we propose fully discrete analogues of a generalized sine-Gordon (gsG) equation . The bilinear equations of the discrete…
Multiple skew orthogonal polynomials and 2-component Pfaff lattice hierarchy
Shi-Hao Li, Bo-Jian Shen, Jie Xiang +1
In this paper, we introduce multiple skew-orthogonal polynomials and investigate their connections with classical integrable systems. By using Pfaffian techniques, we show that mul…
Matrix-valued Cauchy bi-orthogonal polynomials and a novel noncommutative integrable lattice
Shi-Hao Li, Ying Shi, Guo-Fu Yu +1
Matrix-valued Cauchy bi-orthogonal polynomials were proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in four-term recurrence…
Discrete orthogonal ensemble on the exponential lattices
Peter J Forrester, Shi-Hao Li, Bo-Jian Shen +1
Inspired by Aomoto's -Selberg integral, the orthogonal ensemble in the exponential lattice is considered in this paper. By introducing a skew symmetric kernel, the configuration…
An integrable semi-discretization of the modified Camassa-Holm equation with linear dispersion term
Han-Han Sheng, Guo-Fu Yu, Bao-Feng Feng
In the present paper, we are concerned with integrable discretization of a modified Camassa-Holm equation with linear dispersion term. The key of the construction is the semi-discr…
-Pearson pair and moments in -deformed ensembles
Peter J Forrester, Shi-Hao Li, Bo-Jian Shen +1
The generalisation of continuous orthogonal polynomial ensembles from random matrix theory to the -lattice setting is considered. We take up the task of initiating a systematic…
Evaluations of certain Catalan-Hankel Pfaffians via classical skew orthogonal polynomials
Bo-Jian Shen, Shi-Hao Li, Guo-Fu Yu
This paper is to evaluate certain Catalan-Hankel Pfaffians by the theory of skew orthogonal polynomials. Due to different kinds of hypergeometric orthogonal polynomials underlying…
Christoffel transformations for (partial-)skew-orthogonal polynomials and applications
Shi-Hao Li, Guo-Fu Yu
In this article, we consider the Christoffel transformations for skew-orthogonal polynomials and partial-skew-orthogonal polynomials. We demonstrate that the Christoffel transforma…
Two-parameter generalisations of Cauchy bi-orthogonal polynomials and integrable lattices
Xiang-Ke Chang, Shi-Hao Li, Satoshi Tsujimoto +1
In this article, we consider the generalised two-parameter Cauchy two-matrix model and corresponding integrable lattice equation. It is shown that with parameters chosen as …
Matrix integral solutions to the related Leznov lattice equations
Bo-Jian Shen, Guo-Fu Yu
Matrix integrals used in random matrix theory for the study of eigenvalues of matrix ensembles have been shown to provide -functions for several hierarchies of integrable equat…
Rank shift conditions and reductions of 2d-Toda theory
Shi-Hao Li, Guo-Fu Yu
This paper focuses on different reductions of 2-dimensional (2d-)Toda hierarchy. Symmetric and skew symmetric moment matrices are firstly considered, resulting in the differential…
Invariant subspaces of biconfluent Heun operators and special solutions of Painlevé IV
Yik-Man Chiang, Chun-Kong Law, Guo-Fu Yu
We show that there is a full correspondence between the parameters space of the degenerate biconfluent Heun connection (BHC) and that of Painlevé IV that admits special solutions.…
Bright-dark soliton solutions to the multi-component AB system
Zong-Wei Xu, Guo-Fu Yu, Zuo-Nong Zhu
In this paper we investigate the multi-component AB system that comes from the geophysical fluid dynamics. We construct bright-dark soliton solutions through Hirota's bilinear meth…
Integrable discretization of recursion operators and unified bilinear forms to soliton hierarchies
Xingbiao Hu, Guofu Yu, Yingnan Zhang
In this paper, we give a procedure for discretizing recursion operators by utilizing unified bilinear forms within integrable hierarchies. To illustrate this approach, we present u…
Symmetric abstract hypergeometric polynomials
Satoshi Tsujimoto, Luc Vinet, Guo-Fu Yu +1
Consider an abstract operator which acts on monomials according to for and some coefficients. Let be eigenpolynomials…
Galoisian approach to complex oscillation theory of some Hill equations
Yik-Man Chiang, Guo-Fu Yu
We apply Kovacic's algorithm from differential Galois theory to show that all complex non-oscillatory solutions (finite exponential of convergence of zeros) of certain Hill equatio…
Supersymmetry of the quantum rotor
Vincent X. Genest, Luc Vinet, Guo-Fu Yu +1
The quantum rotor is shown to be supersymmetric. The supercharge , whose square equals the Hamiltonian, is constructed with reflection operators. The conserved quantities that c…
A superintegrable discrete harmonic oscillator based on bivariate Charlier polynomials
Vincent X. Genest, Hiroshi Miki, Luc Vinet +1
A simple discrete model of the two dimensional isotropic harmonic oscillator is presented. It is superintegrable with su(2) as its symmetry algebra. It is constructed with the help…
Two integrable differential-difference equations derived from NLS-type equation
Zong-Wei Xu, Guo-Fu Yu, Yik-Man Chiang
Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schröinger equation respec…
On an integrable system related to the relativistic Toda lattice -Bäcklund transformation and integrable discretization
Luc Vinet, Guo-Fu Yu, Ying-Nan Zhang
We study an integrable system related to the relativistic Toda lattice. The bilinear representation of this lattice is given and the Bäckulund transformation obtained. A fully disc…
-Rotations and Krawtchouk polynomials
Vincent X. Genest, Sarah Post, Luc Vinet +2
An algebraic interpretation of the one-variable quantum -Krawtchouk polynomials is provided in the framework of the Schwinger realization of involving…
On complex oscillation theory, quasi-exact solvability and Fredholm Integral Equations
Yik-Man Chiang, Guo-Fu Yu
Biconfluent Heun equation (BHE) is a confluent case of the general Heun equation which has one more regular singular points than the Gauss hypergeometric equation on the Riemann sp…
-1 Krall-Jacobi Polynomials
Luc Vinet, Guo-Fu Yu, Alexei Zhedanov
We study a family of orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue equation involving a third order differential operator of Dunkl-ty…