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 hierarch...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)).展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11601534,11771461 and 11831017)。
文摘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)).
