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Math Colloquium: Universal Wave Patterns
Start Date: 2/14/2018Start Time: 3:00 PM
End Date: 2/14/2018End Time: 4:00 PM

Event Description
Peter Miller, University of Michigan

 

Abstract: A feature of solutions of a (generally nonlinear) field theory can be called "universal" if it is independent of side conditions like initial data. I will explain this phenomenon in some detail and then illustrate it in the context of the sine-Gordon equation, a fundamental relativistic nonlinear wave equation. In particular I will describe some results (joint work with R. Buckingham) concerning a universal wave pattern that appears for all initial data that crosses the separatrix in the phase portrait of the simple pendulum. The pattern is fantastically complex and beautiful to look at but not hard to describe in terms of elementary solutions of the sine-Gordon equation and the collection of rational solutions of the well-known inhomogeneous Painlev\'e-II equation.

Contact Information:
Name: Georgi Medvedev
Email: gsm29@drexel.edu
Location:
Academic Building, Room 302, 101 N 33rd Street, Philadelphia, PA 19104
Audience:
  • Everyone

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