Fronts in Non-Linear Wave Equations with Spatial Inhomogeneity
- When?
- Tuesday 15 November 2011, 16:00 to 17:00
- Where?
- 22AA04
- Open to:
- Students, Staff
- Speaker:
- Chris Knight (Surrey)
Abstract: The non-linear wave equation (sometimes called the non-linear Klien-Gordon equation) is a much studied equation with applications in Josephson transmission lines, dislocations in crystals, DNA processes and much more. It possess many types of solutions which may include stationary front solutions. In this talk we shall consider what effect adding a step-like inhomogeneity has on the stability of such fronts and present some of the results we have derived over the last three years.
Specifically, we shall present a necessary condition for when a front may change stability. This condition is in terms of the length of the various homogeneous intervals and the energy associated with the front in each interval. The necessary condition is in the form of a necessary and sufficient condition for the existence of an eigenvalue zero. Using this condition, we shall provide an example concerning the long-Josephson junction showing that the presence of an inhomogeneity may lead to the existence of a stable non-monotonic stationary front, something that can not exist in the homogeneous case.