42 citations · 62 across the 4 of their papers we have counts for
6 papers
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.
The Extended Toda Hierarchy
Guido Carlet, Boris Dubrovin, Youjin Zhang
We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solut…
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…
Frobenius Manifolds And Virasoro Constraints
Boris Dubrovin, Youjin Zhang
For an arbitrary Frobenius manifold a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation…