Waves in Hamiltonian Systems with Applications in Nonlinear Optics and BECs

摘要：提案0304982 - pi: Todd M. Kapitula， University of New mexico题目：Waves in Hamiltonian Systems with Applications in Nonlinear Optics and becs该提案涉及数学在物理科学的两个重要领域的应用。第一个是集中在光纤阵列的研究和相关的链接逆散射偏微分方程。第二个是在玻色-爱因斯坦凝聚体的区域。这两个主要的推力是通过所谓的埃文斯函数的数学工具联系起来的。埃文斯函数提供了一种理解和利用散射理论求解某些偏微分方程的方法。拟议的光纤工作将对国家通信基础设施产生重大影响，并将支持向家庭和企业提供高速、宽带接入的动力。

Abstract: Proposal 0304982PI: Todd M. Kapitula, University of New MexicoTitle: Waves in Hamiltonian Systems with Applications in Nonlinear Optics and BECsThe 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.