Mathematical Sciences: Integrable Systems in Physics and Engineering

9403597物理与工程中的Kodama可积系统项目的主要主题是A)孤子通信系统，B)。标准形式和对称，和C)。物理和数学中的KP层次和相关主题。在项目A中，主要目的是分析和控制近可积系统中的孤子解，目标是设计和确定一个最可行的模型，用于使用孤子的长距离和高比特率通信系统。在项目B中，目标是根据阶可积系统的对称性，重新表述近似可积系统的庞加莱-杜拉克-伯克霍夫范式理论。在C项目中，重点是将KP和无色散KP理论中发展的求解方法应用于保角场理论领域。这些项目包含了可积系统理论的几个新方向。可积系统理论的最新进展似乎是通过发现它在几个不同的研究领域的应用来证明的，如高能物理、经典和量子场论、非线性光学和无限维李代数的表示理论。这一不断扩大的应用领域为应用数学提供了广泛的研究领域，并促进了现代科学中最重要的跨学科领域的进步。建议的研究与这些研究领域直接相关，我相信这些项目将对应用数学领域的教育和科学与工程人力资源的发展做出一些贡献。

9403597 Kodama Integrable Systems in Physics and Engineering The main themes on the project are A) Soliton Communication Systems, B). Normal Form and Symmetry, and C). KP Hierarchy and Related Topics in Physics and Mathematics. In project A, the main purpose is to analyze and control soliton solutions in nearly integrable systems, and the goal is to design and determine a most feasible model for a long-distance and high-bit-rate communication system using soliton. In project B, the goal is to reformulate the normal form theory of Poincare-Dulac-Birkhoff for nearly integrable system in terms of symmetries of the leading order integrable system. In project C, the emphasis is to apply solution methods developed in the KP and dispersionless KP theories to the field of conformal field theory. These projects contain several new directions of the theory of integrable systems. Recent progress on the theory of integrable systems seems to be demonstrated by finding its applications in several different fields of research, such as high energy physics, classical and quantum field theories, nonlinear optics, and representation theory of infinite dimensional Lie algebra. This expanding area of applications provides a wide variety of studies in applied mathematics, and promotes a progress on interdisciplinary fields which are the most inportant aspects of modern science. The proposed research directly relates with these area of reseach, and I believe that the projects will make several contributions to education in the field of applied mathematics and to development of human resources in science and engineering.