The 71st Midwest Partial Differential Equations Seminar May 11-12, 2013 Room TBA East Hall University of Michigan Ann Arbor, MI   Abstract Detail   Title: Universal Painleve-type critical behavior in the semiclassical sine-Gordon equation The solution to a nonlinear wave equation with given Cauchy data often displays two or more qualitatively different behaviors in different space-time regions, such as having oscillatory and non-oscillatory zones. The boundaries between these regions become well-defined in certain limits (such as long time or small dispersion), making it natural to consider the transition behavior between the two regions. Recently, certain transition regions for solutions of integrable nonlinear wave equations (such as KdV, focusing NLS, and Camassa-Holm) have been universally described for wide classes of initial conditions in terms of Painleve functions. These functions, which are solutions of nonlinear ordinary differential equations, play a role for nonlinear equations analagous to the role played by the classical special functions for linear equations. We will present our result with P. Miller establishing Painleve-type asymptotics in solutions of the semiclassical sine-Gordon equation and show how this has led in turn to new information about certain Painleve functions. Robert Buckingham University of Cincinnati Email:  buckinrt@uc.edu Phone: 734-846-4195   BACK to Speaker Listing BACK to Conference Home   Sponsors National Science Foundation, Department of Mathematics at the University of Michigan