题目：Nonlinear Eigenvalue Problems and Generalized Painlevé Equations
摘要：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.
时间：2024年7月10日 16:00
地点：中国科学院大学中关村校区教学楼N108
主持人：王东教授
报告人：王青海，新加坡国立大学物理系副教授，副系主任。2005年博士毕业于圣路易斯华盛顿大学
