Mathematical Sciences: Integrable Systems and Their PhysicalApplications

这个项目继续研究近可积系统 沿着两条主线：物理应用， 的解决方案的方法的基础上的代数结构的 方程 应用程序集中在与非线性相关的问题 光学. 沿着二线注意力集中在 无色散Lax初值问题的求解 方程，如无色散KP方程。 偏微分方程的可积系统通常 有解，其性质可以精确地确定。 这 与通常的非线性偏微分方程 方程 这里重要的是， 当系统受到干扰时， 可以说，一个伟大的。 处理棘手的问题 出现这样的问题 在非线性光学中（例如，在长距离的设计中）， 使用光纤的通信网络），在 波在非线性声学介质，并在流动周围薄 翅膀

This project continues studies in near-integrable systems along two main lines: physical applications, and the development of solution methods based on the algebraic structure of the equations. Applications focus on problems related to nonlinear optics. Along the second line attention is concentrated on solving the initial value problem for dispersionless Lax equations, such as the dispersionless KP equation. Integrable systems of partial differential equations often have solutions whose properties can be exactly established. This is quite unlike the usual case for nonlinear partial differential equations. What is important here is that often the properties remain when the system is perturbed. Thus one can tell a great deal about otherwise intractable problems. Such problems arise in nonlinear optics (for example, in the design of long-distance communication networks using fiber optics), in the motion of waves in nonlinear acoustic media, and in flows around thin wings.