Let G be arbitrary finite group,define H G· (t;p +,p) to be the generating function of G-wreath double Hurwitz numbers.We prove that H G· (t;p +,p) satisfies a differential equation called the colored cutand...Let G be arbitrary finite group,define H G· (t;p +,p) to be the generating function of G-wreath double Hurwitz numbers.We prove that H G· (t;p +,p) satisfies a differential equation called the colored cutand-join equation.Furthermore,H G·(t;p +,p) is a product of several copies of tau functions of the 2-Toda hierarchy,in independent variables.These generalize the corresponding results for ordinary Hurwitz numbers.展开更多
It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel so...It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel soliton equation hierarchy of integrable coupling system. It indicates that the Kronecker product is an efficient and straightforward method to construct the integrable couplings.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.10425101,10631050)National Basic Research Program of China(973Project)(Grant No.2006cB805905)
文摘Let G be arbitrary finite group,define H G· (t;p +,p) to be the generating function of G-wreath double Hurwitz numbers.We prove that H G· (t;p +,p) satisfies a differential equation called the colored cutand-join equation.Furthermore,H G·(t;p +,p) is a product of several copies of tau functions of the 2-Toda hierarchy,in independent variables.These generalize the corresponding results for ordinary Hurwitz numbers.
基金supported by the Research Work of Liaoning Provincial Development of Education under Grant No. 2008670
文摘It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel soliton equation hierarchy of integrable coupling system. It indicates that the Kronecker product is an efficient and straightforward method to construct the integrable couplings.
