活动类型：

学术活动
活动名称：

Nonlinear Eigenvalue Problems and Generalized Painlevé Equations
地点：

教学楼N108

主讲人：

王东
联系人：

王东
联系方式：

15910781583
开始时间：

2024-07-10 16:00
结束时间：

2024-07-10 18:00
说明:

When solving nonlinear differential equations like the Painlevé transcendentals, by carefully choosing initial conditions, one may obtain a separatrix solution. The nonlinear eigenvalue problem is defined as the discretized initial conditions to be the eigenvalues and the separatrix solutions to be the eigensolutions. In this talk, I will present numerical and analytic results for large initial conditions of the nonlinear eigenvalue problem associate with the first two Painlevé transcendental equations. Then I will generalize Painlevé equations to a class of new nonlinear differential equations, whose movable singularities are all with negative rational powers. I will present a numerical study of the nonlinear eigenvalue problems associated with these generalized Painlevé equations. I will show an intriguing hyperfine structure in the eigenvalues, as well as some open questions.