363 citations · 773 across the 44 of their papers we have counts for
11 papers · 1 filter
On Tautological Flows of Partial Difference Equations
Zhonglun Cao, Si-Qi Liu, Youjin Zhang
We propose a new analyzing method, which is called the tautological flow method, to analyze the integrability of partial difference equations (PEs) based on that of partial diff…
Variational Bihamiltonian Cohomologies and Integrable Hierarchies III: Linear Reciprocal Transformations
Si-Qi Liu, Zhe Wang, Youjin Zhang
For an integrable hierarchy which possesses a bihamiltonian structure with semisimple hydrodynamic limit, we prove that the linear reciprocal transformation with respect to any of…
Reduction of the 2D Toda Hierarchy and Linear Hodge Integrals
Si-Qi Liu, Zhe Wang, Youjin Zhang
We construct a certain reduction of the 2D Toda hierarchy and obtain a tau-symmetric Hamiltonian integrable hierarchy. This reduced integrable hierarchy controls the linear Hodge i…
Virasoro Constraints for Drinfeld-Sokolov hierarchies and equations of Painlevé type
Si-Qi Liu, Chao-Zhong Wu, Youjin Zhang
We construct a tau cover of the generalized Drinfeld-Sokolov hierarchy associated to an arbitrary affine Kac-Moody algebra with gradations $\mathrm{s}\le\mathds{1}$ and derive its…
Drinfeld-Sokolov hierarchies and diagram automorphisms of affine Kac-Moody algebras
Si-Qi Liu, Chao-Zhong Wu, Youjin Zhang +1
For a diagram automorphism of an affine Kac-Moody algebra such that the folded diagram is still an affine Dynkin diagram, we show that the associated Drinfeld-Sokolov hierarchy als…
Fractional Volterra Hierarchy
Si-Qi Liu, Youjin Zhang, Chunhui Zhou
The generating function of cubic Hodge integrals satisfying the local Calabi-Yau condition is conjectured to be a tau function of a new integrable system which can be regarded as a…
On the Drinfeld-Sokolov Hierarchies of D type
Si-Qi Liu, Chao-Zhong Wu, Youjin Zhang
We extend the notion of pseudo-differential operators that are used to represent the Gelfand-Dickey hierarchies, and obtain a similar representation for the full Drinfeld-Sokolov h…
Hamiltonian Structures and Reciprocal Transformations for the -KdV-CH Hierarchy
Ming Chen, Si-Qi Liu, Youjin Zhang
The -KdV-CH hierarchy is a generalization of the Korteweg-de Vries and Camassa-Holm hierarchies parametrized by constants. In this paper we clarify some properties of its…
On Properties of Hamiltonian Structures for a Class of Evolutionary PDEs
Si-Qi Liu, Chao-Zhong Wu, Youjin Zhang
In \cite{LZ2} it is proved that for certain class of perturbations of the hyperbolic equation , there exist changes of coordinate, called quasi-Miura transformations,…
On Quasitriviality and Integrability of a Class of Scalar Evolutionary PDEs
Si-Qi Liu, Youjin Zhang
For certain class of perturbations of the equation , we prove the existence of change of coordinates, called quasi-Miura transformations, that reduce these perturbed…
A 2-Component Generalization of the Camassa-Holm Equation and Its Solutions
Ming Chen, Si-Qi Liu, Youjin Zhang
An explicit reciprocal transformation between a 2-component generalization of the Camassa-Holm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy i…