时间：2022年10月23日

地点：腾讯号：614-567-295    会议密码:  202210

主办单位：中国科学院青年创新促进会数理分会

　　　　　中国科学院数学与系统科学研究院

　　　　　北京大学

 

 

报告人: 李年华 (华侨大学)

报告题目：Baecklund transformation of the Geng-Xue system

摘要：We connect the Geng-Xue system with a negative flow in a modified Boussinesq

hierarchy with the help of a reciprocal transformation. This allows us to derive a Baecklund transformation for the Geng-Xue system from Darboux transformation of the negative modified Boussinesq system. We construct N-Baecklund transformation of the Geng-Xue system resorting to Bianchi's permutability. Furthermore, by considering reductions of the above reciprocal transformation, we discuss Baecklund transformations for the Degasperis-Procesi equation and the Novikov equation.

 

报告人: 刘保平 （北京大学）

报告题目: Wellposedness for the KdV hierarchy

摘要:  The KdV hierarchy is a hierarchy of integrable equations generalizing the KdV equation.  Using the modified Muria transform, we first relate it to the Gardner hierarchy, and by exploiting the idea of approximate flow initiated by Killip-Visan, we show that the whole hierarchy is wellposed for initial data in H^{-1}(R).   This is based on joint work with H.Koch and F. Klaus.

 

报告人: 罗旭丹（中国科学院数学与系统科学研究院）

报告题目: Three-dimensional internal waves in the lower atmosphere
摘要: There are many observations of cloud patterns for the three-dimensional internal waves in the lower atmosphere, which are modelled by the two-dimensional Benjamin-Ono (2DBO) equation with initially truncated and bent line solitary waves. The Whitham modulation theory is employed, and the analytical results are confirmed numerically. Sometimes, when the variation in the transverse direction is not weak, the 2DBO model has to be generalized to the isotropic situation. We further propose the Benjamin-Ono-Benney-Luke equation to describe these wave phenomena.

 

报告人: 生云鹤 （吉林大学）

报告题目：Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebras

摘要：In this talk, first we introduce the notion of quadratic Rota-Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie bialgebras and quadratic Rota-Baxter Lie algebras of nonzero weight. Then we introduce the notions of matched pairs, bialgebras and Manin triples of Rota-Baxter Lie algebras of arbitrary weight, and show that Rota-Baxter Lie bialgebras, Manin triples of Rota-Baxter Lie algebras and certain matched pairs of Rota-Baxter Lie algebras are equivalent. The coadjoint representations and quadratic Rota-Baxter Lie algebras play important roles in the whole study. 

 

报告人: 田守富 （中国矿业大学）

报告题目：On soliton solutions and long-time asymptotic behavior to some integrable models: Riemann-Hilbert approach

报告摘要：In this talk, I will briefly introduce the development of the research on soliton solutions and long-time asymptotic to integrable systems, and the major work about our team to the long-time asymptotic behavior of some integrable models. It mainly contains the following several aspects: the nonlinear steepest descent method and its applications to long-time asymptotic of integrable equations, the $\bar{\partial}$-steepest descent method to soliton resolution and asymptotic stability of integrable equations.

 

报告人: 徐建 （上海理工大学）

报告题目：负阶WKI型可积方程的渐近分析
摘要：本次报告，主要介绍利用Riemann-Hilbert方法研究负阶WKI型可积系统的初值问题的长时间渐近行为。首先由于所考虑的Lax对属于负阶的WKI型，谱分析的过程与经典的AKNS型Lax对有一些不同之处，我们将在本报告中介绍如何通过适当的方式处理，将初值问题转化为相应的Riemann-Hilbert问题，然后利用非线性速降法得到相应的长时间渐近，由于可积性，与通过PDE的方式得到的结果相比，可以给出精确的首项渐近结果。

 

报告人: 徐帅侠 （中山大学）

报告题目：Gap probability of higher order Airy process and the second Painlev\'e hierarchy

摘要：In this talk, we study one-parameter family of determinants of the higher order Airy kernel. The determinants describe new universal class of distributions which are higher order analogues of the Tracy-Widom distribution.  Particularly,  the determinants can be expressed in terms of solutions to the second Painlev\'{e} hierarchy. We derive large gap asymptotics of the determinants up to and including the constant term with the parameter in (0, 1). This talk is based on joint work with Yifan Hao, Jun Xia, Yuqiu Zhao and Lun Zhang.