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(Dec. 25) Nonlinear Eigenvalue Problems and Generalized Painlevé Equations

Last updated :2017-12-21

Topic: Nonlinear Eigenvalue Problems and Generalized Painlevé Equations
Speaker: Dr. Wang Qinghai
(National University of Singapore)
Time: 16:00-17:00, Monday, December 25, 2017
Venue: Room 519, New Mathematics Building, Guangzhou South Campus, SYSU

Abstract:
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.