05.05.2015, 14:15-15:05: Malcolm Brown (Cardiff, Wales, UK): Uniqueness for an inverse scattering problem
Abstract: The Camassa-Holm equation is used to model breaking waves. It is an integrable system and as such the evolution of its solution is determined by an inverse scattering problem. We shall discuss the question of uniqueness for this problem.
This is joint work with Christer Bennewitz (Lund, Sweden) and Rudi Weikard (Birmingham AL, USA).
05.05.2015, 15:10-16:00: Ian Wood (Canterbury, England, UK): Some spectral results for waveguides
Abstract: We study a spectral problem for the Laplacian in a weighted space which is related to the propagation of electromagnetic waves in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic medium. The defect is infinitely extended and aligned with one of the coordinate axes. This perturbation introduces guided mode spectrum inside the band gaps of the fully periodic, unperturbed spectral problem. We use variational arguments to prove that guided mode spectrum can be created by arbitrarily small perturbations to the coefficient in the equation. After performing a Floquet decomposition in the axial direction of the waveguide, we study the spectrum created by the perturbation for any fixed value of the quasi-momentum.
19.05.2015 Seminar "The Reve's Puzzle Solved?" 06bis
23.06.2015 Seminar "The Reve's Puzzle Solved?" 08
14.07.2015 Seminar "The Reve's Puzzle Solved?" 9bis