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Asymptotics for the Korteweg-de Vries equation and perturbations using Riemann-Hilbert methods

Random Matrix Theory and Its Applications I September 13, 2010 - September 17, 2010

September 17, 2010 (02:30 PM PDT - 03:10 PM PDT)
Speaker(s): Tom Claeys
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

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Abstract Small dispersion asymptotics for solutions to the Korteweg-de Vries equation can be obtained using Riemann-Hilbert problems. In critical regimes, this leads to asymptotic expansions in terms of Painlev\'e transcendents. I will give an overview of this procedure, and I will discuss some obstacles that occur when considering non-integrable perturbations of the Korteweg-de Vries equation. This is based on joint work with Tamara Grava, and on joint work in progress with Tamara Grava and Ken McLaughlin.
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