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

• 作者: Weiqiang He Hua-Zhong Ke Chao-Zhong Wu
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（6）
• 所属期刊栏目: Articles
• 页码范围: 1245-1262
• 页数: 18页
• 语种: 英文

摘要

In this paper we report some explicit evolutionary PDEs of the Drinfeld-Sokolov hierarchy of type E(1)6,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 E6 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 F4(1).