scientific article; zbMATH DE number 7594563

DOI10.11845/sxjz.2020011aMaRDI QIDQ5037952

Shi-Hao Li, Bao Wang, Xiaomin Chen, Xiang-Ke Chang

Publication date: 29 September 2022

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

orthogonal polynomials random matrices integrable systems discrete moving frame multipeakons

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Cites Work

Painlevé V and time-dependent Jacobi polynomials
On the ``Favard theorem and its extensions
Schur flow for orthogonal polynomials on the unit circle and its integrable discretization
The Cauchy two-matrix model
Relating the Bures measure to the Cauchy two-matrix model
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Discrete moving frames and discrete integrable systems
Discrete spectral transformations of skew orthogonal polynomials and associated discrete integrable systems
Vector orthogonal relations. Vector QD-algorithm
Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials
On the relation between the full Kostant-Toda lattice and multiple orthogonal polynomials
Toda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation
Padé-type approximation and general orthogonal polynomials
Solitons and infinite dimensional Lie algebras
Bi-orthogonal polynomials on the unit circle, regular semi-classical weights and integrable systems
Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions
Cauchy biorthogonal polynomials
Dynamics and interpretation of some integrable systems via multiple orthogonal polynomials
The integration of semi-infinite Toda chain by means of inverse spectral problem
Bäcklund transformations and their applications
An integrable chain and bi-orthogonal polynomials
The spectrum of coupled random matrices
Integrable equations arising from motions of plane curves. II.
Multipeakons and the classical moment problem
Pfaff $\tau$-functions
Partial-skew-orthogonal polynomials and related integrable lattices with Pfaffian tau-functions
Moment modification, multipeakons, and nonisospectral generalizations
Lax integrability and the peakon problem for the modified Camassa-Holm equation
An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type
Toda versus Pfaff lattice and related polynomials.
The Korteweg-de Vries equation and beyond
Orthogonal polynomial approach to discrete Lax pairs for initial boundary-value problems of the QD algorithm
Matrix integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomials
Surfaces on Lie groups, on Lie algebras, and their integrability (with an appendix by Juan Carlos Alvarez Paiva)
Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
Spectral transformation chains and some new biorthogonal rational functions
Isospectral flows related to Frobenius-Stickelberger-Thiele polynomials
Group foliation of finite difference equations
Painlevé III and a singular linear statistics in Hermitian random matrix ensembles. I.
Universality conjecture and results for a model of several coupled positive-definite matrices
Isogonal deformation of discrete plane curves and discrete Burgers hierarchy
Toda chain, Stieltjes function, and orthogonal polynomials
A two-component generalization of the Camassa-Holm equation and its solutions
Cauchy-Laguerre two-matrix model and the Meijer-$G$ random point field
Integrable discrete time chains for the Frobenius-Stickelberger-Thiele polynomials
A generalized nonisospectral Camassa-Holm equation and its multipeakon solutions
Multipeakons of a two-component modified Camassa-Holm equation and the relation with the finite Kac-van Moerbeke lattice
The Cauchy two-matrix model, C-Toda lattice and CKP hierarchy
On the associated orthogonal polynomials
Peakons, strings, and the finite Toda lattice
Faces of Relativistic Toda Chain
Discrete Systems and Integrability
Hamiltonian evolutions of twisted polygons in $\mathbb{RP}^n$
Discrete KdV and Discrete Modified KdV Equations Arising from Motions of Planar Discrete Curves
About several classes of bi-orthogonal polynomials and discrete integrable systems
Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions
Matrix Integrals and Several Integrable Differential-Difference Systems
Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves
Determinant structure of non-autonomous Toda-type integrable systems
Fox H-kernel and θ-deformation of the Cauchy Two-Matrix Model and Bures Ensemble
An extension of integrable peakon equations with cubic nonlinearity
A new integrable equation with cuspons and W/M-shape-peaks solitons
Discrete Curves in and the Toda Lattice
Integrable peakon equations with cubic nonlinearity
Painlevé VI and the Unitary Jacobi Ensembles
Linear algebra algorithms as dynamical systems
Generalizations of the Camassa–Holm equation
KP Hierarchies of Orthogonal and Symplectic Type–Transformation Groups for Soliton Equations VI–
Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
Multi-peakons and a theorem of Stieltjes
Discrete-time Volterra chain and classical orthogonal polynomials
String-orthogonal polynomials, string equations, and 2-Toda symmetries
Introduction to Classical Integrable Systems
Breakdown of the Camassa-Holm equation
Multi-peakon solutions of the Degasperis–Procesi equation
Orthogonal and Symplectic Matrix Integrals and Coupled KP Hierarchy
Nonperturbative two-dimensional quantum gravity
An integrable shallow water equation with peaked solitons
Degasperis–Procesi peakon dynamical system and finite Toda lattice of CKP type
Orthogonal Polynomials and Painlevé Equations
Schrödinger Equations in Nonlinear Systems
On moving frames and Toda lattices of BKP and CKP types
Integrable dynamics of a discrete curve and the Ablowitz–Ladik hierarchy
The partition function of the Bures ensemble as theτ-function of BKP and DKP hierarchies: continuous and discrete
Extrapolation and Rational Approximation
A new integrable two-component system with cubic nonlinearity
Degasperis-Procesi peakons and the discrete cubic string
Discrete mKdV and discrete sine-Gordon flows on discrete space curves
An Extension of Kakutani's Theorem on Infinite Product Measures to the Tensor Product of Semifinite w ∗ -Algebras
A Class of Matrix Ensembles
Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces