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The onset of instabilities in partial differential equations

  • 3 February 2022
  • 1pm-2pm
  • Online

About this event

From a mathematical point of view, the description of natural phenomena that evolve through time and space is encapsulated as solutions of nonlinear partial differential equations. Given that the task of finding explicit solutions is very difficult, a more qualitative approach often allows us to predict the behaviour of the phenomena without having to exhibit a solution for the equation. We are particularly interested in stability, a central problem in the field of nonlinear wave propagation, and a fairly broad subject.

In this talk we introduce the topics being developed, which deal with the characterisation of the onset of instabilities for nonlinear integrable equations through the study of their stability spectra, a structure recently introduced in the literature. As an initial discussion, we compare the stability spectrum to the Lax spectrum of the scalar and vector nonlinear Schroedinger equations and give an overview of further directions for the project.

This research seminar will be given by Newton International Fellow Dr Priscila Leal da Silva.

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Kieran Teasdale
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