363 citations · 1.3k across the 53 of their papers we have counts for
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Generalized Frobenius Manifold Structures on the Orbit Spaces of Affine Weyl Groups II
Lingrui Jiang, Si-qi Liu, Yingchao Tian +1
This is a sequel to arXiv:2506.13656, in which an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups is presented.…
Generalized Frobenius Manifold Structures on the Orbit Spaces of Affine Weyl Groups I
Lingrui Jiang, Si-Qi Liu, Yingchao Tian +1
We present an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups, and prove that their monodromy groups are parabo…
Variational Bihamiltonian Cohomologies and Integrable Hierarchies I: Foundations
Si-Qi Liu, Zhe Wang, Youjin Zhang
This series of papers is devoted to the study of deformations of Virasoro symmetries of the principal hierarchies associated to semisimple Frobenius manifolds. The main tool we use…
Super tau-covers of bihamiltonian integrable hierarchies
Si-Qi Liu, Zhe Wang, Youjin Zhang
We consider a certain super extension, called the super tau-cover, of a bihamiltonian integrable hierarchy which contains the Hamiltonian structures including both the local and no…
Bihamiltonian Cohomologies and Integrable Hierarchies II: the Tau Structures
Boris Dubrovin, Si-Qi Liu, Youjin Zhang
Starting from a so-called flat exact semisimple bihamiltonian structures of hydrodynamic type, we arrive at a Frobenius manifold structure and a tau structure for the associated pr…
Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials
Boris Dubrovin, Ian A. B. Strachan, Youjin Zhang +1
For the root systems of type and , we generalize the result of \cite{DZ1998} by showing the existence of Frobenius manifold structures on the orbit spaces of the ex…
Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case
Si-Qi Liu, Youjin Zhang
We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for th…
The Inversion Symmetry of the WDVV Equations and Tau Functions
Si-Qi Liu, Dingdian Xu, Youjin Zhang
For two solutions of the WDVV equations that are related by the inversion symmetry, we show that the associated principal hierarchies of integrable systems are related by a recipro…
On Symmetries of the WDVV Equations
Dingdian Xu, Youjin Zhang
For two solutions of the WDVV equations that are related by two types of symmetries of the equations given by Dubrovin, we show that the associated principal hierarchies of integra…
Jacobi Structures of Evolutionary Partial Differential Equations
Si-Qi Liu, Youjin Zhang
In this paper we introduce the notion of infinite dimensional Jacobi structure to describe the geometrical structure of a class of nonlocal Hamiltonian systems which appear natural…
Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures
Boris Dubrovin, Si-Qi Liu, Youjin Zhang
The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of…
Bihamiltonian Systems of Hydrodynamic Type and Reciprocal Transformations
Ting Xue, Youjin Zhang
We prove that under certain linear reciprocal transformation, an evolutionary PDE of hydrodynamic type that admits a bihamiltonian structure is transformed to a system of the same…
Extended affine Weyl groups and Frobenius manifolds -- II
Boris Dubrovin, Youjin Zhang, Dafeng Zuo
For the root system of type and , we generalize the result of \cite{DZ1998} by showing the existence of a Frobenius manifold structure on the orbit space of the extended…
On Hamiltonian perturbations of hyperbolic systems of conservation laws
Boris Dubrovin, Si-Qi Liu, Youjin Zhang
We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs. Under certain genericity a…
On the Quasitriviality of Deformations of Bihamiltonian Structures of Hydrodynamic Type
Si-Qi Liu, Youjin Zhang
We prove in this paper the quasitriviality of a class of deformations of the one component bihamiltonian structures of hydrodynamic type.
Deformations of Semisimple Bihamiltonian Structures of Hydrodynamic Type
Si-Qi Liu, Youjin Zhang
We classify in this paper infinitesimal quasitrivial deformations of semisimple bihamiltonian structures of hydrodynamic type.
Virasoro Symmetries of the Extended Toda Hierarchy
Boris Dubrovin, Youjin Zhang
We prove that the extended Toda hierarchy of \cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators $L_…
Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
Boris Dubrovin, Youjin Zhang
We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of…