Mathematical Sciences: Nonlinear Wave Motion

这个项目将发展非线性问题的连贯结构，并获得物理问题中出现的方程的解。所采用的技术包括渐近和摄动分析、数值计算和精确解。在精确分析领域中，散射逆变换方法尤为重要。这项工作具有一般的特点，因此具有广泛的适用性。应用的例子包括波在表面波和内波中的传播，非线性光学中的自聚焦和孤子传播，爱因斯坦真空方程的精确简化，以及数值计算的各个方面。

This project will develop coherent structures in nonlinear problems and obtain solutions to equations arising in physical problems. The techniques to be employed include asymptotic and perturbation analysis, numerical computation, and exact solutions. Especially important in the realm of exact analysis is the method of inverse scattering transform. This work has generic features and, consequently, broad applicability. Examples of applications include wave propagation in surface and internal waves, self focussing and soliton propagation in nonlinear optics, exact reductions of Einstein's vacuum equations, and aspects on numerical computation.