论文标题
较高的加泰罗尼亚属数量和延长非线性施罗丁格层次结构
Higher genera Catalan numbers and Hirota equations for extended nonlinear Schroedinger hierarchy
论文作者
论文摘要
We consider the Dubrovin--Frobenius manifold of rank $2$ whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the enumeration of maps on surfaces, ribbon graphs, Grothendieck's dessins d'enfants, strictly monotone Hurwitz numbers, or lattice points in the moduli spaces of curves.刘，张和周认为，这种dubrovin--frobenius歧管的完整分区函数是扩展的非线性schrödinger层次结构的tau功能，这是kadomtsev-petverviashvili层次的特定合理降低的扩展。我们证明了他们的猜想的一个版本，专门为givental-milanov方法提供了允许构建分区函数的hirota二次方程，然后从中衍生出LAX表示。
We consider the Dubrovin--Frobenius manifold of rank $2$ whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the enumeration of maps on surfaces, ribbon graphs, Grothendieck's dessins d'enfants, strictly monotone Hurwitz numbers, or lattice points in the moduli spaces of curves. Liu, Zhang, and Zhou conjectured that the full partition function of this Dubrovin--Frobenius manifold is a tau-function of the extended nonlinear Schrödinger hierarchy, an extension of a particular rational reduction of the Kadomtsev--Petviashvili hierarchy. We prove a version of their conjecture specializing the Givental--Milanov method that allows to construct the Hirota quadratic equations for the partition function, and then deriving from them the Lax representation.
