Mathematical Sciences: Integrable Systems in Physics and Engineering

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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.