42 citations · 62 across the 4 of their papers we have counts for
4 papers · 1 filter
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.
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…