On the Drinfeld-Sokolov hierarchy of type E_(6)^((1))and its topological solution  

作　　者：Weiqiang He Hua-Zhong Ke Chao-Zhong Wu 

机构地区：[1]School of Mathematics,Sun Yat-sen University,Guangzhou 510275,China

出　　处：《Science China Mathematics》2021年第6期1245-1262,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11601534,11771461 and 11831017)。

摘　　要：In this paper we report some explicit evolutionary PDEs of the Drinfeld-Sokolov hierarchy of type E_(6)^((1)),and show how the unknown functions in these PDEs are related to the tau function.Moreover,for this hierarchy we compute its topological solution of formal series up to a certain degree,whose coefficients of monomials give the Fan-Jarvis-Ruan-Witten invariants for the E_(6) simple singularity.Based on such results we also derive several explicit evolutionary PDEs and some low-degree terms of the topological solution for the Drinfeld-Sokolov hierarchy of type F_(4)^((1)).

关 键 词：Drinfeld-Sokolov hierarchy tau function topological solution 

分 类 号：O175.2[理学—数学]