Mathematical Sciences: Nearly Integrable Nonlinear Wave Phenomena:Theory and Applications"

数学科学：近可积非线性波现象：理论与应用》

• 批准号: 9403596
• 负责人: M Forest
• 金额: $ 11.5万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9403596&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nearly; Integrable; Nonlinear

9403596 Forest/Overman The primary project relates to the equations of nonlinear Schrodinger type which govern pulse transmission in fiber optics. Scalar NLS is the model equation for monomode fibers, while coupled systems of NLS equations describe birefringent fibers, switching devices, fiber-fiber links, etc. While the integrable theory and near-integrable perturbation methods are well-developed for scalar NLS, these fundamental results are still open for coupled NLS equations. We propose to develop several interconnected projects in this proposal: the spectral transform construction of pulse train solutions for coupled NLS; explicit characterization of integrable instabilites; numerical codes to implement the spectral transform in conjunction with full pde codes for the precise optical perturbations of coupled NLS pdes; nearly integrable perturbation methods to understand the observed simulations. Ultimately, our goal is to predict and understand the robust, optimal transmission and switching limits of present fiber optic technology, in cooperation with and driven by industry collaborators. Fiber optics technology is fundamental to modern communications and the electronic superhighway. Advantages in this technology can clearly be achieved by accurate models and simulation of the transmission along these various fibers. While long-distance communication lines are now on sound mathematical and engineering grounds, various new fibers and applications lead to more complicated model equations and quite different issues need to be understood. The fundamental governing equations for fiber optics consist of a single nonlinear Schrodinger (NLS) equation, while the newer applications are governed by coupled NLS equations. The theory and nonlinear diagnostic tools for the solitons of NLS are NOT yet known for the coupled NLS pdes--these valuable methods are precisely the goals of our proposal. We intend to develop these methods on the equations of practical interes t, with the collaboration of optics experts in academics and industry, and focused on the problems of technological concern.

9403596 Forest/Overman 主要项目涉及控制光纤中脉冲传输的非线性薛定谔方程。 标量NLS是单模光纤的模型方程，而耦合系统的NLS方程描述双折射光纤，开关器件，光纤-光纤链路等，而可积理论和近可积微扰方法是发达的标量NLS，这些基本结果仍然是开放的耦合NLS方程。我们建议开发几个相互关联的项目在这个建议：光谱变换耦合NLS的脉冲串解决方案的建设;明确的可积不稳定性的表征;数值代码，以实现光谱变换与完整的耦合NLS偏微分方程的精确光学扰动的偏微分方程代码;近可积的扰动方法来理解所观察到的模拟。最终，我们的目标是预测和了解目前光纤技术的鲁棒性，最佳传输和交换限制，与行业合作者合作并由行业合作者驱动。 光纤技术是现代通信和电子高速公路的基础。这种技术的优点可以通过精确的模型和沿沿着这些不同光纤的传输的模拟来清楚地实现。虽然长距离通信线路现在已经有了坚实的数学和工程基础，但各种新的光纤和应用会导致更复杂的模型方程，并且需要理解完全不同的问题。 光纤光学的基本控制方程由单个非线性薛定谔（NLS）方程组成，而较新的应用则由耦合NLS方程组成。NLS孤子的理论和非线性诊断工具对于耦合NLS偏微分方程还不清楚-这些有价值的方法正是我们建议的目标。我们打算与学术界和工业界的光学专家合作，在实际感兴趣的方程上开发这些方法，并专注于技术关注的问题。