活动类型: | 学术活动 |
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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. |