Mathematical Sciences: Nonlinear Waves

点击翻译按钮获取中文摘要

9404528 Goodman We will study nonlinear dispersive waves by combining the normal forms technique of dynamical systems with nonlinear harmonic analysis. We will study multi-D perturbations of plane wave solutions of systems of reaction-diffusion equations, attempting to relate simple effective equations to the full equations. We will develop and analyze numerical methods for stochastic differential equations with special attention to boundaries. Nonlinear dispersive waves include waves on the surface of water and sound waves in a crystal lattice of atoms. Reaction diffusion equations describe, among other things, flames. Understanding of instabilities of flames is important, for example, in chemical engineering. Stochastic differential equations are used to model molecules in modern drug design, stock price and interest rate movements (important in New York City), and many other things. Efficient and accurate simulation technology is sorely needed in these areas.