Location: room 611 of the Wiskunde building (campus De Uithof) Budapestlaan 6, Utrecht.

Date and time: Thursday, May 27, 2010 15:30-16:30. The lecture is preceded by coffee, tea, and cookies from 15.00 to 15.30 hour in the same room.

The Evans function and the stability of travelling waves


Jitse Niesen

(Leeds)

Abstract: Travelling waves are solutions to partial differential equations that move as a whole without changing their shape. The stability of these waves determines the fate of small perturbations of the travelling wave. Linearization of the differential equation around the travelling wave yields a linear differential operator, and its spectrum gives information about the stability of the wave. The Evans function is a tool for analyzing the eigenvalues of such operators. It is related to the shooting method for solving Sturm-Liouville equations in its simplest form, but it also provides a topological invariant: its winding number equals the first Chern number of the unstable bundle. This talk reviews the Evans function and how they can be used to assess the stability of traveling waves.

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