Global analysis of dispersion and resonance of nonlinear waves

从相空间解的初始数据和拓扑信息出发，构建了确定非线性波偏微分方程通解时空行为的理论，并将时空动力学完全分类到略高于基态的能级。这是一个数学上严格的描述，仅仅基于方程，散射，孤子和爆炸的机制，这是非线性波的典型行为，以及它们之间的过渡。

I constructed a theory to determine space-time behavior of general solutions for partial differential equations describing nonlinear waves, from the initial data and topological information on the solution in the phase space, and completely classified space-time dynamics up to an energy level slightly above that of the ground state. It is a mathematically rigorous description, based solely on the equation, of the mechanism of scattering, soliton and blow-up, which are typical behavior of nonlinear waves, and of transitions among them.