Скачать или смотреть Eduard-Wilhelm Kirr: Nonlinear coherent structures at the Fredholm boundary

Title: Nonlinear coherent structures at the Fredholm boundary

Abstract: Wave Equations are ubiquitous models in nature, ranging from sound and surface waves to optical signals and Bose-Einstein Condensates. One of their most important features are coherent structures i.e., solutions which propagate without changing shape or evolve in a periodic manner. Some well known examples are solitons propagating at the boundary between two fluids or in optical fibers, Bose-Einstein Condensates, etc. The existence of coherent structures and their stability have been intensely studied over the last two centuries with methods covering the whole mathematical spectrum. However, there are no methods which can systematically find all coherent structures supported by a given equation. In my talk I will propose such a method and show its results on a few examples.