Mathematical Sciences: Phase Shift Phenomenon for Perturbed Evolution Equations and Applications to Nonlinear Optics

9626672阿尔伯 在这个项目中，辛几何和几何力学的方法将被用来分析非线性波系统的相空间几何和研究孤子微扰理论的新技术。特别是，调查计划研究几何和马斯洛夫阶段的非线性波系统和KAM型理论的动力系统与相空间叶的非线性紧凑不变品种。 几何力学使用辛微分几何的现代语言重新表述了经典力学的一部分。它在运动产生、运动控制和非线性光学等领域有着广泛的应用前景。

9626672 Alber In this project methods of symplectic geometry and geometric mechanics are to be used to analyze the phase-space geometry of nonlinear wave systems and to investigate new techniques for soliton perturbation theory. In particular, the investigator plans to study geometric and Maslov phases of nonlinear wave systems and a KAM type theory for dynamical systems with phase spaces foliated by the nonlinear compact invariant varieties. Geometric mechanics reformulates parts of classical mechanics using the modern language of symplectic differential geometry. It has potential applications in a variety of applications including locomotion generation, motion control and nonlinear optics.