Title 1 : From integrable spatial discrete hierarchy to integrable nonlinear PDE hierarchy
Speaker: Zuonong Zhu ( Shanghai Jiao Tong University )
Time: Fri, Apr.26, 2021, PM:20:00-21:00
Location: Tencent Conference
Meeting Number: 260 177 127
Title 2 : The kink solutions of the SIdV equation and the associated surfaces
Speaker: Prof. Jingsong He ( Institute for Advanced Study, Shenzhen University )
Time: Sun, Apr.28, 2021, PM:14:30-15:30
Location: Tencent Conference
Meeting Number: 627 396 862
Title 3: Matrix integral solutions to the related Leznov lattice equations
Speaker: Prof. Guofu Yu ( Shanghai Jiao Tong University )
Time: Sun, Apr.28, 2021, PM:15:30-16:30
Location: Tencent Conference
Meeting Number: 627 396 862
Title 4: Local waves and integrable deep learning algorithms
Speaker: Prof. Yong Chen ( East China Normal University )
Time: Wed, Apr.31, 2021, PM:15:00-16:00
Location: Tencent Conference
Meeting Number: 574 117 344
Inviter: Dr. Liming Ling
Abstract1:
In this talk, we will address the topic that from integrable spatial discrete hierarchy to integrable nonlinear PDE hierarchy. We will review that how to get the integrability theory of the KdV hierarchy from the integrability of spatial discrete KdV hierarchy.
Abstract2:
In this talk, we study a new non-linear integrable equation, , which is invariant under scaling of dependent variable and was called the SIdV equation, see [Commun. Nonlinear Sci. Numeric. Simulat. 17 (2012) 4155.] The order-n kink solution of the SIdV equation, which is associated with the n-soliton solution of the Korteweg-de Vries equation, is constructed by using the n-fold Darboux transformation (DT) from zero “seed” solution. Moreover, we also proivde the evolution scenarios of surfaces of revolution associated with the kink-type solutions of the SIdV, where the kink-type solutions play the role of a metric. We put forward two kinds of evolution scenarios for surfaces of revolution associated with two types of kink-type metric (solution) and we study the key properties of these surfaces.
Abstract3:
Matrix integrals used in random matrix theory for the study of eigenvalues of matrix ensembles have been shown to provide τ-functions for several hierarchies of integrable equations. In this talk, we construct the matrix integral solutions to the Leznov lattice equation, the related discrete Leznov lattice and the Pfaffianized lattice systems, respectively. We demonstrate that the partition function of Jacobi unitary ensemble is a solution to the semi-discrete Leznov lattice and the partition function of Jacobi orthogonal/symplectic ensemble gives solutions of the Pfaffianized Leznov lattice.