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Universal Wave Breaking in the Semiclassical Sine-Gordon Equation

Peter Miller
Institution: 
University of Michigan Ann Arbor
Schedule: 
Wednesday, December 16, 2020 - 16:00
Location: 
Online
Location: 
Zoom
Abstract: 

The sine-Gordon equation has slowly-modulated librational wave solutions that are approximated at leading-order by a Whitham averaging formalism. The Whitham modulation equations are an elliptic quasilinear system whose solutions develop singularities in finite time. We show that when the solution of the Whitham system develops a generic type of gradient catastrophe singularity, the solution of the sine-Gordon equation locally takes on a universal form, independent of initial data and described in terms of the real tritronquée solution of the Painlevé-I equation and a two-parameter family of exact solutions of sine-Gordon that represent space-time localized defects on an otherwise periodic background wave.  This is joint work with Bing-Ying Lu.

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