The proposal concerns the applications of mathematics to two important areas of physical sciences. The first is centered on the study of arrays of optical fibers and associated links to inverse scattering for partial differential equations. The second is in the area of Bose-Einstein condensates. Both major thrusts are related by the mathematical tool of the so-called Evans function. The Evans function provides a way to understand and use scattering theory to solve certain partial differential equations.
The proposed work on optical fibers is positioned to have significant impact on the national communications infrastructure and will support the drive to deliver high speed, broad bandwidth access to homes and businesses.
