Seminar Event Detail


Integrable Systems and Random Matrix Theory

Date:  Monday, February 12, 2018
Location:  1866 East Hall (4:00 PM to 5:00 PM)

Title:  Rational Solutions of Painleve Equations

Abstract:   Most solutions of the famous Painleve differential equations are highly transcendental, yet all but the Painleve-I equation admit particular solutions that are elementary rational functions. These particular solutions are important in diverse applications, including the description of equilibrium patterns of fluid vortices, universal phenomena in nonlinear wave theory, electrochemistry, and string theory. This talk will illustrate some features of these particular solutions, describe how they may be obtained by iterated Backlund transformations or via the solution of appropriate Riemann-Hilbert problems, and focus attention on recent and ongoing efforts by several researchers to study families of rational Painleve solutions in the asymptotic limit of large degree.

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Speaker:  Peter Miller
Institution:  University of Michigan

Event Organizer:   Guilherme Silva    silvag@umich.edu

 

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