44 citations · 196 across the 19 of their papers we have counts for
19 papers
Stationary reduction method based on nonisospectral deformation of orthogonal polynomials, and discrete Painlevé-type equations
Xiao-Lu Yue, Xiang-Ke Chang, Xing-Biao Hu
In this work, we propose a new approach called ``stationary reduction method based on nonisospectral deformation of orthogonal polynomials" for deriving discrete Painlevé-type (d-P…
Hermite--Padé approximations with Pfaffian structures: Novikov peakon equation and integrable lattices
Xiang-Ke Chang
Motivated by the Novikov equation and its peakon problem, we propose a new mixed type Hermite--Padé approximation whose unique solution is a sequence of polynomials constructed wit…
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 …
Isospectral flows related to Frobenius-Stickelberger-Thiele polynomials
Xiang-Ke Chang, Xing-Biao Hu, Jacek Szmigielski +1
The isospectral deformations of the Frobenius-Stickelberger-Thiele (FST) polynomials introduced in [32](Spiridonov et al. Commun. Math. Phys. 272:139--165, 2007 ) are studied. For…
Vibrations of an elastic bar, isospectral deformations, and modified Camassa-Holm equations
Xiang-Ke Chang, Jacek Szmigielski
Vibrations of an elastic rod are described by a Sturm-Liouville system. We present a general discussion of isospectral (spectrum preserving) deformations of such a system. We inter…
Construction of New Generalizations of Wynn's Epsilon and Rho Algorithm by Solving Finite Difference Equations in the Transformation Order
Xiang-Ke Chang, Yi He, Xing-Biao Hu +2
We construct new sequence transformations based on Wynn's epsilon and rho algorithms. The recursions of the new algorithms include the recursions of Wynn's epsilon and rho algorith…
Partial-skew-orthogonal polynomials and related integrable lattices with Pfaffian tau-functions
Xiang-Ke Chang, Yi He, Xing-Biao Hu +1
Skew-orthogonal polynomials (SOPs) arise in the study of the n-point distribution function for orthogonal and symplectic random matrix ensembles. Motivated by the average of charac…
Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type
Xiang-Ke Chang, Xing-Biao Hu, Shi-Hao Li
In this paper, we propose a finite Toda lattice of CKP type (C-Toda) together with a Lax pair. Our motivation is based on the fact that the Camassa-Holm (CH) peakon dynamical syste…
An Application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type
Xiang-Ke Chang, Xing-Biao Hu, Shi-Hao Li +1
The Novikov equation is an integrable analogue of the Camassa-Holm equation with a cubic (rather than quadratic) nonlinear term. Both these equations support a special family of we…
The dynamics of conservative peakons in the NLS hierarchy
Stephen C. Anco, Xiangke Chang, Jacek Szmigielski
Using the tri-hamiltonian splitting method, the authors of [Anco and Mobasheramini, Physica D, 355:1--23, 2017] derived two -invariant nonlinear PDEs that arise from the hier…
Liouville integrability of conservative peakons for a modified CH equation
Xiang-Ke Chang, Jacek Szmigielski
The modified Camassa-Holm equation (also called FORQ) is one of numerous of the Camassa-Holm equation possessing non-smoth solitons () as special solutions. The…
Lax integrability and the peakon problem for the modified Camassa-Holm equation
Xiangke Chang, Jacek Szmigielski
Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks…
Lax Integrability of the Modified Camassa-Holm Equation and the Concept of Peakons
Xiangke Chang, Jacek Szmigielski
In this Letter we propose that for Lax integrable nonlinear partial differential equations the natural concept of weak solutions is implied by the compatibility condition for the r…
An inverse problem for the modified Camassa-Holm equation and multi-point Padé approximants
Xiangke Chang, Jacek Szmigielski
In this Letter the main steps in the inverse spectral construction of a family of non-smooth solitons (peakons) to the modified Camassa-Holm equation are oulined. It is shown that…
Multipeakons of a two-component modified Camassa-Holm equation and the relation with the finite Kac-van Moerbeke lattice
Xiangke Chang, Xingbiao Hu, Jacek Szmigielski
A spectral and the inverse spectral problem are studied for the two-component modified Camassa-Holm type for measures associated to interlacing peaks. It is shown that the spectral…
Hankel determinant solutions to several discrete integrable systems and the Laurent Property
Xiang-Ke Chang, Xing-Biao Hu, Guoce Xin
Many discrete integrable systems exhibit the Laurent phenomenon. In this paper, we investigate three integrable systems: the Somos-4 recurrence, the Somos-5 recurrence and a system…
About several classes of bi-orthogonal polynomials and discrete integrable systems
Xiangke Chang, Xiaomin Chen, Xingbiao Hu +1
By introducing some special bi-orthogonal polynomials, we derive the so-called discrete hungry quotient-difference (dhQD) algorithm and a system related to the QD-type discrete hun…
A generalized nonisospectral Camassa-Holm equation and its multipeakon solutions
Xiangke Chang, Xiaomin Chen, Xingbiao Hu
Motivated by the paper (Beals, Sattinger and Szmigielski, Adv. Math. 154 (2000) 229--257), we propose an extension of the Camassa-Holm equation, which also admits the multipeakon s…
Integrable Discretization of Soliton Equations via Bilinear Method and Bäcklund Transformation
Yingnan Zhang, Xiangke Chang, Juan Hu +2
In this paper, we present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota's bilinear method. This approach is mainly based on the compatibility be…