258 citations · 1.5k across the 56 of their papers we have counts for
58 papers
Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method
Boris Dubrovin, Daniele Valeri, Di Yang
For each affine Kac-Moody algebra of rank , , or , and for every choice of a vertex , , of the corresponding Dynkin diagram, by usi…
Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality
Boris Dubrovin, Di Yang, Don Zagier
For each of the simple Lie algebras , or , we show that the all-genera one-point FJRW invariants of -type, after multiplication by suitab…
Remarks on intersection numbers and integrable hierarchies. I. Quasi-triviality
Boris Dubrovin, Di Yang
Explicit expression for quasi-triviality of scalar non-linear PDE is under consideration.
Matrix resolvent and the discrete KdV hierarchy
Boris Dubrovin, Di Yang
Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-functio…
On a class of compact perturbations of the special pole-free joint solution of KdV and
B. Dubrovin, A. Minakov
We consider perturbations of the special pole-free joint solution of the Korteweg--de Vries equation and equation $u_{xxxx}+10u_x^…
On tau-functions for the KdV hierarchy
Boris Dubrovin, Di Yang, Don Zagier
For an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent…